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GIFT   OF 


AERIAL  NAVIGATION 


PART  I.  THE  COMPASS 
PART  II.  THE  MAP 


ISSUED  BY  THE 

DIVISION  OF  MILITARY  AERONAUTICS,  U.  S.  ARMY 
WASHINGTON,  D.  C. 


-99- 


WASHINGTON 

GOVERNMENT  PRINTING  OFFICE 
1918 


t  i 


AERIAL  NAVIGATION. 

Part  I.   The  Compass, 

Introduction , 5 

The  compass 7 

True  courses 8 

Magnetic  courses 10 

Relation  between  true  and  magnetic  courses 11 

Compass  courses 13 

Relation  between  magnetic  and  compass  courses 14 

Relation  between  true  and  compass  courses 15 

Course  setting  with  allowance  for  wind 19 

To  find  direction  and  velocity  of  wind 20 

Radius  of  action  in  a  given  direction 22 

Bearings: 

Definition 23 

Fixing  position  of  a  machine 24 

Instruments:    _ 

Bearing  plate 25 

Aircraft  course  and  distance  indicator 27 

Illustrative  problem 31 

Checks 34 

Technique 35 

Compass  adjustment -. 38 

Deviation  card 40 

3 


AERIAL  NAVIGATION. 

PART  II.   The  Map. 


Page. 

Introduction  

43 

Scales  

46 

Time  scales  , 

.    47 

Metric  system  , 

50 

Conventional  signs  

52 

Contours  

52 

Location  of  points  

58 

Coordinates  

59 

British  maps  

61 

French  maps  

63 

4 

AERIAL  NAVIGATION. 


PART  I. 

THE  COMPASS. 


INTRODUCTION, 

When  a  pilot  travels  by  airplane  from  his  aerodrome  to  a  point 
beyond  the  horizon,  he  has  need  of  navigation  by  means  of  map 
and  compass.  The  problem  of  passing  from  one  point  to  another  is 
evidently  one  of  distance  and  direction.  In  both  respects  the  pilot 
is  liable  to  go  wrong.  Without  proper  care  he  may  go  many  miles 
out  of  the  way  either  by  going  too  far  or  by  taking  the  wrong  course. 
He  may  even  land  within  the  German  lines;  he  may  mistake  a 
German  aerodrome  for  his  own;  he  may  land  at  his  own  aerodrome 
and  think  that  he  is  lost.  At  any  rate,  without  proper  care  he  is 
apt  not  to  accomplish  his  mission. 

There  are  several  sources  of  error  which  must  be  guarded  against. 
For  one  thing,  the  influence  of  the  wind;  for  another,  the  failure  of 
the  compass  to  point  to  true  north;  for  another,  failure  on  the  part 
of  the  pilot  to  fly  for  a  reasonable  length  of  time.  It  is  evident,  for 
example,  that  a  pilot  proceeding  on  a  course  30  miles  in  length  at 
the  rate  of  90  m.  p.  h.  in  still  air  must  not  travel  for  anywhere  near 
an  hour.  He  must  not  go  on  and  on  in  the  hope  of  reaching  his 
destination  some  time  or  other. 

The  influence  of  the  wind  is  felt  by  an  airplane  exactly  as  the 
influence  of  a  current  of  water  is  felt  by  a  boat.  If  a  man  rows  a 
boat  across  a  river,  pointing  the  boat  straight  across,  he  is  drifted 
downstream.  If  the  current  is  swift  the  downstream  drift  is  con- 
siderable. So  a  wind  is  a  stream  or  current  of  air  which  drifts  the 
airplane  in  the  direction  it  is  blowing. 

5 


6  AEP-IAL  NAVIGATION. 

The1,  ^y  teat  of  the  error  which  may  be  caused  by  the  wind  is 
illustrated  as  follows : 


FIG.  1. 

Suppose  a  ship  has  a  speed  of  60  m.  p.  h.  and  the  desired  course 
is  true  south,  a  distance  of  30  miles.  Suppose  there  is  a  west  wind 
blowing  at  the  rate  of  30  m.  p.  h.  If  the  pilot  does  not  allow  for  this 
wind  he  will  find  himself,  at  the  end  of  a  half  hour,  15  miles  to  the 
east  of  his  destination  and  badly  confused  as  to  direction.  If  he 
tries  to  return  to  his  own  aerodrome  by  flying  north,  he  will  be  30 
miles  out  of  his  way,  supposing  he  has  made  no  errors  with  respect 
to  compass  and  watch. 

On  page  31,  a  problem  will  be  worked  out  in  detail  showing  how  a 
pilot  lays  out  his  course  so  as  to  fly  from  his  aerodrome  to  a  given  des- 
tination. If  desired,  it  may  be  read  in  this  connection  or  it  may  be 
read  in  its  place  after  the  general  discussion.  Following  the  dis- 
cussion of  this  special  problem  will  be  found  a  paragraph  showing 
how  the  pilot  may  check  his  course  roughly  for  distance  and  direc- 
tion and  another  showing  how  he  may  develop  technique  necessary 
for  navigation.  These  paragraphs  may  be  read  when  desired,  either 
before  or  after  the  general  discussion. 


AERIAL 

THE  COMPASS: 


The  magnetic  compass  consists  of  three  principal  parts — a  bowl,  a 
needle,  and  a  card. 

The  bowl  is  composed  of  nonmagnetic  metal.  In  its  center  is  a 
post  or  pivot,  and  on  the  top  of  this,  which  is  jeweled  to  reduce 
friction  to  a  minimum,  is  suspended  a  needle,  or  system  of  needles. 
These  are  attached  to  the  lower  side  of  a  circular  card.  This  card  is 
free  to  rotate  under  the  influence  of  the  needles  and  take  up  a  definite 
position  with  reference  to  the  earth's  magnetism.  In  aircraft  com- 
passes the  bowl  is  filled  with  a  nonfreezing  liquid,  generally  alcohol 
or  kerosene,  which  takes  some  of  the  weight  of  the  needle  and  card 


off  the  pivot  and  also  serves  to  damp  the  oscillations  and  vibrations 
of  the  needle. 

On  its  outer  edge  the  card  is  marked  off  into  360  degrees.  Start- 
ing with  north  as  the  zero  point,  the  figuring  runs  clockwise  through 
east,  south,  and  west,  to  north  again. 

The  value  of  the  compass  is  that  the  needle  gives  us  a  fixed  direc- 
tion (compass  north)  from  which  to  measure  the  direction  our  ship 
is  taking.  The  needle  does  not  follow  the  changes  in  direction  of 
the  ship.  On  the  contrary,  the  ship  turns  around  the  needle.  The 
direction  of  the  machine  is  shown  by  the  lubber's  line,  which  is  a 


NAVIGATION. 


tc\the  compass  bowl  or  a  line  painted  on 
the  inside  bt  the  "oowi.1  '  ^he'lubfter's  line  and  the  center  of  the  com- 
pass give  the  direction  of  the  fore  and  aft  axis  of  the  machine.  Since 
the  needle  points  north,  the  angle  from  the  needle  to  the  lubber's 
line  represents  the  course  of  the  machine.  This  angle  is  measured 
in  degrees  on  the  card  in  a  clockwise  direction  from  north.  Thus, 
if  the  lubber's  line  is  opposite  90,  the  compass  course  is  east;  if  the 
lubber's  line  is  opposite  45,  the  course  is  northeast,  etc. 

It  is  convenient  to  remember  the  number  of  degrees  corresponding 
to  each  of  the  " cardinal"  and  "quadrantal"  points  of  the  compass. 


N. 
i  \ 


40° 


FIG.  6. 

The  cardinal  points— N.  E.  S.  W.— correspond  to  0,  90,  180,  and  270 
degrees.  The  quadrantal  points — NE.  SE.  SW.  NW.— correspond  to 
45,  135,  225,  and  315  degrees.  With  these  points  in  mind,  it  is  easy 
to  S3e,  for  example,  that  285°  indicates  a  direction  slightly  north  of 
west,  and  that  185°  indicates  a  direction  just  west  of  south. 

TRUE  COURSES. 

The  problem  of  aerial  navigation  is  to  fly  from  one  point  to  another. 
This  may  be  divided  into  two  problems — one  of  distance  and  one  of 
direction.  The  problem  of  distance  will  be  discussed  later  under 
" Map  reading." 

The  direction  of  one  point  from  another  is  fixed.  In  order  to 
describe  it-  in  an  exact  way  we  must  measure  the  angle  which  this 
direction  makes  with  another  direction  that  is  known  in  advance. 
In  navigation  problems  this  known  direction  is  taken  as  north. 


AERIAL  NAVIGATION.  9 

The  value  of  the  angle  which  the  given  direction  makes  with  north 
measuring  clockwise  from  north  is  called  the  course  from  the  point 
of  departure  to  the  destination. 

For  example,  if  A  and  B  are  two  points  on  the  map,  the  course 
from  A  to  B  is  the  number  of  degrees  in  the  angle  NAB,  where  the 
direction  AN  is  the  direction  of  the  meridians  on  the  map.  In  the 
figure,  the  course  from  A  to  B  is  40°.  Courses  relative  to  the  map  are 
known  as  "true"  courses. 

N 


)220 

FIG.  4. 

Similarly,  the  statement  "the  course  from  A  to  B  is  220°"  means 
that  the  angle  NAB  measures  220°  in  a  clockwise  direction  and 
AN  is  the  direction  of  true  north  from  A. 

It  is  advisable  to  practice  at  once,  laying  off  courses  from  one 
point  to  another,  choosing  a  certain  direction  as  North  and  measur- 
ing the  number  of  degrees  clockwise  from  this  direction  in  order  to 
get  an  idea  of  the  values  of  different  angles. 


FIG.  5. 

Example  1:  If  north  is  represented  by  the  arrow,  what  is  the  course 
from  A  to  B?    Measure  with  protractor.1 

*A  good  protractor  for  this  work  is  made  by  a  transparent  piece  of  celluloid  4  or  5 
inches  square  on  which  is  marked  a  circle  graduated  in  degrees.  At  the  center  of 
the  circle  a  silk  thread  is  attached  which  when  stretched  taut  will  give  the  course 
from  the  center  to  any  desired  point  relative  to  the  line  joining  the  center  of  the 
circle  and  the  point  marked  zero  or  360°.  Practice  with  this  protractor  is  valuable 
in  giving  a  student  a  knowledge  of  the  values  oi  angles. 
77023 — 18 2 


10 


AERIAL  NAVIGATION. 


Example  2:  Choosing  a  certain  direction  as  north,  draw  figures  to 
represent  the  following:  The  course  from  A  to  B  is  15° ,  315°,  175°, 
210°,  0°,  90°,  270°. 

Example  3:  From  any  map -in  your  possession  make  up  a  number 
of  examples  to  illustrate  the  course  from  one  point  to  another  and 
work  them  out.  For  example,  given  a  map  of  the  region  about 
Paris,  determine  the  true  course  from  Nanteuil  to  Betz,  from  Nan- 
teuil  to  Senlis,  from  Meaux  to  Coulommiers. 

MAGNETIC  COURSES. 

The  magnetic  course  from  A  to  B,  like  the  true  course,  is  the  angle 
NAB  measured  clockwise  from  north,  only  in  this  case  AN  is  the 
direction  of  magnetic  north. 

N 


FIG.  6. 
VARIATION. 

The  compass  needle  does  not  point  to  the  geographic  North  Pole, 
but  (when  unaffected  by  local  magnetism)  to  a  point  known  as  the- 
magnetic  North  Pole,  situated  near  the  northern  extremity  of  the 
American  Continent.  The  difference  between  the  two  directions 
of  magnetic  and  true  north  is  known  as  variation  or  declination. 
It  is  described  as  easterly  or  westerly,  according  as  the  compass 
needle  points  to  the  east  or  west  of  true  north.  It  is  measured  in 
degrees — 15°  west,  8°  east,  etc. 

Variation  on  the  east  coast  of  the  United  States  near  Washington  is 
about  8°  west,  and  that  in  southern  California  is  about  15°  east.  In 
northern  France  it  is  approximately  13°  west.  The  variation  as 
given  on  the  Ypres  sheet  of  the  map  of  Belgium  is  13°  34',  1916. 


AERIAL  NAVIGATION. 


11 


The  date  of  the  variation  is  usually  given,  for  the  reason  that  the 
variation  changes  from  year  to  year,  though  generally  not  by  more 
than  a  few  minutes. 

RELATION  BETWEEN  TRUE  AND  MAGNETIC  COURSES. 

In  northern  France,  at  present,  the  magnetic  courses  differ  from  the 
"true1'  courses  by  something  like  13°.  If  a  pilot  did  not  allow  for 
this  fact,  he  would  be  about  14  miles  out  of  the  way  in  a  60-mile 
flight,  supposing  that  all  his  other  calculations  were  correct. 

The  variation  of  the  compass  presents  two  problems:  (1)  Given 
the  true  course  and  a  certain  variation  to  find  the  magnetic  course; 


Variation  15°W 


Variation  8°E 


FIG.  7. 


FIG. 


(2)  given  the  magnetic  course  and  the  variation  to  find  the  true 
course.  In  either  case  the  angle  is  read  from  north  (magnetic  or  true) 
in  a  clockwise  direction.  From  figure  7  it  is  evident  that  if  the 
variation  is  15°  west,  a  clockwise  reading  from  AM  will  be  15°  greater 
than  a  clockwise  reading  from  AN.  Therefore  if  the  variation  is  west 
and  the  true  course  is  given,  say  45°,  to  find  the  corresponding  mag- 
netic course,  add  15°,  getting  60°  as  a  result.  On  the  other  hand,  if 
the  magnetic  course  is  given,  say  90°,  to  find  the  true  course  subtract 
15°,  getting  75°  as  a  result. 

If  the  variation  is  east,  the  reverse  holds,  namely,  add  the  varia- 
tion in. passing  from  magnetic  to  true;  subtract  the  variation  passing 
from  true_to_magnetic. 


12 


AERIAL  NAVIGATION. 


The  difficulty  in  variation  problems  lies  in  the  fact  that  they  are 
so  simple.  It  is  necessary  only  to  add  or  subtract  a  certain  amount, 
but  very  frequently  one  adds  this  amount  when  he  should  subtract 
it,  and  vice  versa.  To  reduce  these  errors  to  a  minimum  it  is  advisable 
to  work  out  a  large  number  of  problems,  taking  care  at  the  outset  to 
make  as  few  mistakes  as  possible  in  order  that  a  correct  habit  may  be 
formed  and  carrying  on  the  practice  over  a  long  period  of  time. 

It  is  advisable  at  the  outset  to  draw  a  figure  in  every  case.  From 
the  figures  it  will  be  apparent  that  if  the  variation  is  west,  the 
magnetic  reading  is  greater  than  the  true;  and  if  the  variation  is  east, 
the  magnetic  reading  will  be  less  than  the  true.  This  relation  may 
be  remembered  by  the  words — 

Variation  WEST  COMPASS  BEST. 
Variation  EAST  COMPASS  LEAST. 


In  remembering  these  phrases  the  word  "variation*'  may  be 
omitted  if  desired.  The  student  should  adopt  that  method  of  solving 
the  problems  which  works  best  for  him  in  practice.  If  possible  he 
should  visualize  the  angle  NAM. 

The  following  examples  are  given  by  way  of  illustration: 

Example  1:  The  true  course  is  54°  var.  13°  W.,  then  the  magnetic 
course  is  67°. 

Example  2:  Magnetic  course  is  300°,  var.  8°  E. ;  true  course  is  308° . 

Example  3:  True  course  10°,  var.  15°  E.;  magnetic  course  355°. 

Example  4:  Magnetic  course  15°,  var.  10°  W.;  true  course  5°. 


: 


AERIAL  NAVIGATION. 


COMPASS  COURSES. 

DEVIATION. 


13 


The  compass  in  an  airplane  is  affected  by  the  iron  and  steel  in  the 
plane  so  that  in  general  it  does  not  point  to  magnetic  north,  but 
"  deviates"  from  it  slightly  according  to  the  course  the  airplane 
is  heading.  This  means  that  the  compass  course,  the  angle  the 
pilot  must  fly  by,  is  different  from  both  the  true  and  magnetic 
courses. 


Delation  3* 


FIG.  10. 


M         M 


represented 6y 
/lr,q/e  M/t.C. 


FIG.  11. 

This  deviation  is  similar  to  variation.  As  variation  is  divergence 
from  true  north,  so  deviation  is  divergence  from  magnetic  north. 

It  is  described  in  the  same  way  as  variation,  3°  E.,  5°  W.,  etc. 
The  deviation  of  an  airplane  compass  varies,  both  in  magnitude  and 
direction,  for  different  positions  of  the  airplane.  It  must  be  cor- 


14  AERIAL  NAVIGATION. 

rected  by  means  of  magnets  placed  near  the  compass  in  such  a 
manner  as  to  counteract  the  local  influence  on  the  needle.  All 
compasses  have  receptacles  for  these  correcting  magnets.  This 
process  is  known  as  "swinging  the  compass"  and  will  be  described 
later  in  more  detail  under  "Compass  adjustment." 

RELATION  BETWEEN  MAGNETIC  AND  COMPASS  COURSES. 

Let  us  suppose  for  the  present  that  the  deviation  corresponding 
to  a  given  course  is  known.  Two  problems  are  presented:  (1)  Given 
the  magnetic  course  and  the  corresponding  deviation  to  find  the 
compass  course;  (2)  given  the  compass  course  and  the  corresponding 
deviation  to  find  the  magnetic  course. 

A  number  of  problems  should  be  worked  out,  making  as  few  mis- 
takes as  possible  at  the  outset  and  practicing  over  a  long  period  of 
time.  As  with  variation  problems,  a  figure  should  be  drawn  at  first 
in  each  case.  The  words — 

Deviation  WEST  COMPASS  BEST, 
Deviation  EAST  COMPASS  LEAST, 

express  the  relation  between  magnetic  and  compass  readings.  That 
is,  when  the  deviation  is  west,  the  compass  reading  is  greater  than 
the  magnetic.  When  the  deviation  is  east,  the  compass  reading  is 
less  than  the  magnetic.  In  remembering  these  phrases  the  word 
"deviation"  may  be  omitted  if 'desired.  A  student  should  find  the 
method  which  works  best  for  him  in  practice  and  adopt  it  to  the 
exclusion  of  any  other  method. 

The  following  examples  are  given  by  way  of  illustration: 

Example  1.  Given  magnetic  210°,  deviation  3°  W.;  compass  is 
213°.  (Compass  best.) 

Example  2.  Given  magnetic  359°,  deviation  2°  W.;  compass  is  I6. 
(Compass  best  361°.) 

Example  3.  Given  magnetic  355°,  deviation  2°  E.;  compass  is 
353°.  (Compass  least.) 

Example  4.  Given  compass  5°,  deviation  2°  E.;  magnetic  is  7°. 
(Compass  least.) 

Example  5.  Given  compass  35°,  deviation  3°  W.,  magnetic  is  32°. 
(Compass  best.) 


AERIAL  NAVIGATION.  15 

RELATION  BETWEEN  TRUE  AND  COMPASS  COURSES. 

ORDER  OP  PROCEDURE. 

We  have  found  the  relation  (1)  between  true  and  magnetic,  (2) 
between  magnetic  and  compass.  A  combination  of  these  two 
enables  us  to  find  the  relation  (3)  between  true  and  compass.  This 
relation  between  true  and  compass  is  determined  by  the  relation 
which  each  bears  to  magnetic.  Thus,  magnetic  is  an  auxiliary  con- 
necting true  and  compass.  Whether  we  pass  from  compass  to  true 
or  from  true  to  compass,  we  must  pass  through  magnetic.  The  order 
is  either  true,  magnetic,  compass;  or  compass,  magnetic,  true.  There 
is  no  other  order. 

This  means  that  when  we  pass  from  true  to  compass  we  apply 
variation  first  and  deviation  second ;  when  we  pass  from  compass  to 


FIG.  12. 

true  we  apply  deviation  first  and  variation  second.  A  failure  to 
observe  this  order  of  procedure  might  result  in  large  errors. 

The  following  examples  are  given  by  way  of  illustration  with  the 
deviation  given  for  each  course.  The  explanation  is  made  quite 
full  for  the  sake  of  review.  A  number  of  similar  examples  should 
be  worked  out. 

Given  true  course  35°,  variation  15°  N.,  deviation  3°  E.,  find 
compass. 

The  angle  NOX,  35°,  is  the  true  course  of  the  ship.  It  is  evident 
that  if  we  wish  to  obtain  the  magnetic  course  of  the  ship,  which  is 
MOX,  we  must  add  the  15°  variation,  the  angle  NOM.  This  gives 
us  50°  magnetic  course.  Again,  if  we  wish  to  obtain  the  compass 
course  of  the  ship  (that  is,  the  angle  its  direction  makes  with  the 


16 


AERIAL  NAVIGATION. 


compass  needle,  the  angle  it  must  fly  by),  we  must  subtract  from 
MOX  the  angle  MOC,  our  3°  deviation,  which  gives  us  47°,  compass 
course. 

It  will  also  be  clear  that  if  the  line  OM  lay  to  the  right  (east)  of 
the  line  ON,  that  is,  if  our  variation  were  15°  east  instead  of  15° 
west,  we  should  have  to  subtract  MON  from  NOX,  in  order  to  find 
MOX.  In  that  case  the'  result  would  be  20°,  magnetic  course. 
Similarly,  if  OC  lay  to  the  west  of  OM  instead  of  to  the  east  of  it, 
we  should  have  to  add  the  angle  COM  to  MOX  in  order  to  obtain 
COX,  the  compass  bearing,  which  in  that  case  would  be  23°. 


-Q)2fs' 


FIG.  13. 

Suppose,  with  reference  to  above  figure,  the  compass  course,  47°, 
COX,  is  given  us,  and  we  wish  to  find  the  true  course,  NOX.  In 
that  case,  we  shall  have  to  add  our  3°  easterly  deviation  to  find  the 
magnetic  course,  50°,  and  then  subtract  our  15°  westerly  variation 
from  that  to  get  true  course,  which  will  be  35°. 

Example.  Given  true  course  255°,  variation  8°  E.,  deviation  2° 
W.  To  find  compass  course. 

Until  the  thing  is  thoroughly  understood,  it  is  always  well  to  draw 
a  diagram. 

NOX,  our  true  course,  is  255°.  To  find  MOX  we  must  subtract 
8°,  which  gives  us  247°,  magnetic  course.  To  find  COX  we  must 
add  2°,  which  gives  us  249 °,  compass  course. 


AERIAL  NAVIGATION. 


17 


Example:  Given  compass  course  357°,  deviation  2°  W.,  variation 
5°  E.     To  find  true  course. 
Start  out  by  drawing  the  angle  we  know,  COX,  357°. 


FIG.  14. 


The  deviation  being  2°  west,  the  C  line  must  be  2°  to  the  left,  or 
west  of  the  M  line.     Then  draw  the  M  line  2°  to  the  east  of  the  C  line. 

M   C  M 


357 


FIG  15. 

To  find  magnetic  course,  MOX,  subtract  the  2°  westerly  deviation. 
This  gives  355°,  magnetic  course. 

But  the  variation  being  5°  east,  the  N  line  must  be  drawn  in  5° 
to  the  left,  or  west,  of  the  M  line.  This  makes  it  identical  with  the 
77023—18 3 


18  AERIAL  NAVIGATION. 

X  line,  the  direction  in  which  our  ship  is  heading.  In  other  words, 
we  add  5°  easterly  variation  and  get  360°,  true  bearing.  The  ship 
is  headirg  exactly  true  north,  though  according  to  the  compass  it 
is  heading  3°  to  the  west  of  north. 

It  should  always  be  borne  in  mind  that  a  course  is  a  clockivise 
angle  from  north.  In  all  cases,  what  it  is  desired  to  find  is  the 
ang^.e  which  the  X  line,  the  direction  of  the  ship,  makes  with  one 
of  the  three  lines  around  north,  the  N,  M,  or  C  lines. 

Variation  and  deviation  are  sometimes  referred  to  as  plus  or 
minus  quantities,  e.  g.,  —13,  +4.  Deviation  cards  are  frequently 
made  out  in  this  way.  It  is  always  well  to  beware  of  such  signs, 
for  their  meaning  is  relative  to  something  variable.  Whether  we 
should  add  or  subtract  westerly  deviation,  for  example,  depends 
entirely  on  which  way  we  are  going,  from  true  to  compass  or  compass 
to  true. 

Deviation,  it  must  be  remembered,  is  always  considered  with 
reference  to  magnetic,  never  with  reference  to  true.  We  have  no 
concern  with  the  ang'e  NOG.  . 

Remember,  therefore,  when  working  from  true  to  compass,  to 
apply  variation  first,  then  deviation.  Conversely,  when  working 
from  compass  to  true,  apply  deviation  first,  then  variation. 

This  would  not  be  necessary  if  deviation  were  a  constant  quantity 
for  every  point  of  the  compass.  It  actually  varies  considerably, 
often  between  quite  closely  adjacent  points,  so  that  a  deviation 
correction  applied  to  a  direction  representing  a  true  course  might 
differ  radically  from  the  deviation  which  should  be  applied  for 
that  course  with  the  appropriate  variation  added  or  subtracted. 

For  example,  compass  course  240°,  variation  15°  W.,  deviation 
for  240°,  2°  E.  To  find  true  course. 

Suppose  we  correct  for  variation  first  and  subtract  our  15°  westerly 
variation,  getting  225°.  Then,  desiring  to  apply  correction  for 
deviation  and  looking  at  our  deviation  card,  we  might  discover, 
especially  if  the  compass  had  not  been  particularly  well  adjusted, 
that  the  proper  deviation  for  225°  was  4°  W.,  instead  of  2°  E.  It 
is  clear  that  the  result  would  be  different  from  that  obtained  by 
following  the  proper  order.  In  the  former  case  it  would  be  221°, 
in  the  latter  227°. 

In  the  following  examples  the  table,  page  41,  is  used. 

Example  1:  Given  true  course  equals  230°,  variation  13°  W. 
"Find  compass.  Magnetic  is  243°,  corresponding  deviation  is  4°  E. 
Compass  is  239°. 


AERIAL  NAVIGATION. 


19 


Example  2 :  Given  true  47°,  variation  10°  E.  Find  compass. 
Magnetic  is  37°,  corresponding  deviation  4°  W.  Compass  is  41°. 

Working  from  compass  to  true  we  proceed  as  follows: 

Example  3:  Given  compass  255°,  variation  13°  W.  Find  true. 
Corresponding  deviation  is  2°  E.,  magnetic  257°.  True  244°. 

Example  4:  Given  compass  44°,  variation  8°  E.  Find  true. 
Corresponding  deviation  4°  W.,  magnetic  40°.  True  is  48°. 

COURSE  SETTING  WITH  ALLOWANCE  FOR  WIND. 

In  actual  practice,  it  is  generally  not  sufficient  to  set  a  course 
from  the  map  as  described  above.  It  is  necessary  to  make  due 
allowance  for  the  wind,  which,  if  blowing  with  any  considerable 


velocity,  will  deflect  the  airplane  from  its  course  and  take  it  in  a 
direction  far  from  the  desired  one.  The  problem  is  difficult  as  the 
wind  varies  in  velocity  and  direction  with  time  and  altitude. 
However,  once  the  direction  and  velocity  of  the  wind  are  known, 
it  is  not  difficult  to  map  out  one's  course  so  as  to  allow  for  its  influence. 
Suppose,  for  example,  we  wish  to  fly  a  course  which  we  find  to 
be  25°  true,  in  a  machine  whose  air  speed  is  60  m.  p.  h.  The  wind 
at  the  height  at  which  we  wish  to  fly  is  blowing  at  20  m.  p.  h.  from 
300°  true. 

On  the  map  itself,  or  on  a  separate  sheet  of  paper,  draw  a  line 

connecting  the  points  of  departure  and  destination,  AB,  at  an  angle 

'  of  55°  from  true  north.     Then  from  A,  the  point  of  departure,  plot 

out  a  line  directly  down  wind,  proportionate  in  length  to  the  number 

of  miles  the  wind  blows  per  hour,  AC. 


20  AERIAL  NAVIGATION. 

From  C,  swing  a  line  equal  in  length  to  the  air  speed  of  the  machine, 
in  miles  per  hour,  till  it  cuts  the  line  AB.  Mark  this  point  D. 

The  line  CD  gives  the  course  to  be  steered  and  air  speed,  AD  gives 
the  course  to  be  made  good  ('"track")  and  ground  speed,  while  AC 
gives  the  speed  and  direction  of  the  wind.  The  line  AD  is  evidently 
the  "resultant"  of  the  "components"  AC  and  CD. 

From  A  draw  a  line  parallel  to  CD,  any  convenient  length,  AB'. 
The  direction  of  this  line  will  give  the  course  to  be  steered.  In  this 
case,  it  is  38°  true.  Then  correct  for  variation  and  deviation,  in  the 
usual  way. 

The  machine  will  fly  over  the  course  AB,  but  it  will  be  headed 
("crabbing")  in  the  direction  ABX.  The  divergence  of  this  from 
the  course  to  be  made  good  ("track")  will  just  counteract  the  side- 
ways drift  caused  by  the  wind. 

For  the  return  journey  a  new  course  must  be  set  and  a  new  figure 
drawn.  It  will  not  do  to  fly  back  over  the  reverse  of  the  outward 
course.  The  course  must  also  be  altered  in  the  air  if  it  is  discovered 
that  the  wind  has  changed  much  in  direction  or  velocity.  This  can 
be  done  in  the  air  by  the  process  described  above,  but  it  is  generally 
easier  to  use  the  course  and  distance  indicator.  (See  page  30.) 

The  line  AD  represents  the  ground  speed  of  the  machine  in  miles 
per  hour.  It  is  often  desirable  to  find  this,  in  order  to  get  some  idea 
of  how  far  you  can  fly  on  your  supply  of  petrol .  It  is  easily  found  on 
the  drawing  by  measuring  it  off  on  the  same  scale  as  that  used  in 
drawing  the  lines  AC  and  CD.  In  this  case  it  is  about  67  miles  per 
hour.  The  scale  used  on  the  above  drawing  is  one-sixteenth  inch  to 
a  mile,  or  sixteen  miles  to  an  inch;  this  will  be  found  to  be  a  conve- 
nient scale  when  working  in  miles .  When  working  under  the  metric 
system,  the  scale  of  1  millimeter  to  a  mile  is  convenient. 

It  will  be  noted  that  in  the  above  drawing  the  ground  speed  is 
greater  than  the  air  speed.  This  is  because  the  wind  is  blowing  more 
from  behind  the  machine  than  from  in  front  of  it,  and  is  conse- 
quently pushing  it  forward  rather  than  back.  If  the  wind  tends  to 
blow  the  machine  back,  the  ground  speed  line  will  of  course  be 
shorter  than  the  air  speed  line. 

TO  FIND  DIRECTION  AND  VELOCITY  OF  WIND. 

In  the  foregoing  problem  it  is  assumed  that  the  force  and  direction 

of  the  wind  are  known.     In  practice  these  data  are  often  furnished 

to  the  airdrome  by  an  adjacent  meteorological  station,  but  this  is  not 

'  always  the  case.     It  is  sometimes  necessary  for  a  pilot  to  go  up,  fly 


AERIAL  NAVIGATION. 


21 


over  a  short  known  course,  and  from  the  data  thereby  obtained  work 
out  on  pap?r  the  desired  information.  This  is  done  by  a  process 
similar,  or  rather  converse  to,  the  one  just  described. 

AB  represents  the  bearing  between  the  two  known  points,  such 
as  two  prominent  buildings,  for  example;  if  the  course  is  flown  at 
night,  two  srarchlights  are  used.  The  bearing  AB  is  55°  true. 
Starting  over  A  and  keeping  the  point  B  always  in  sight,  the  pilot 
flics  toward  it  in  as  straight  a  line  as  possible.  If  there  is  a  wind 
blowing,  he  will  find  himself  "crabbing;"  that  is,  in  order  to  fly 
over  the  prescribed  track,  he  will  have  to  alfcr  the  direction  or  course 
of  his  machine.  In  this  case  we  will  call  the  course  AC,  38°  true. 
Naturally  the  pilot  can  not  take  true  readings  from  his  compass,  but 
will  have  to  correct  his  compass  reading  for  deviation  and  variation 


FIG.  17. 

in  order  to  get  a  true  reading.  We  will  suppose  that  this  has  been 
done,  and  that  the  true  course  thus  found  is  38°. 

It  is  also  n?cessary  to  have  the  air  speed  and  ground  speed  of  the 
machine.  The  air  speed  is  read  from  the  air  speed  meter;  suppose 
in  this  case  it  is  80  m.  p.  h.  For  obtaining  the  ground  speed  a  stop 
watch  is  necessary.  By  it  the  pilot  discovers  the  number  of  seconds 
it  takes  him  to  fly  a  known  distance  on  his  track.  Suppcse  he 
traverses  1  mile  in  55  S3conds.  To  turn  this  into  miles  per  hour,  it  is 
only  necessary  to  divide  3,600  (the  number  of  seconds  in  an  hour) 
by  55.  This  gives  65  and  a  fraction. 

Now  the  pilot  lays  off  a  unit  of  length  proportional  to  his  air  speed 
on  his  course,  and  a  corresponding  unit  representing  his  ground  speed 
on  his  track.  A  line  joining  the  two  will  give  the  direction  and  velo- 
city of  the  wind,  in  miles  per  hour. 

This  is  the  line  DE,  which  on  being  measured  is  found  to  be  pro- 
portional to  25  miles  in  length,  with  a  true  bearing  of  350°. 


22  AERIAL  NAVIGATION. 

(The  measurements  in  the  diagram  are  on  a  scale  J  inch  equals  10 
miles.  Any  scale  will  do,  regardless  of  the  length  we  draw  AB,  so 
long  as  the  same  scale  is  used  for  all  measurements  concerned.) 

Remember  that  the  direction  of  a  wind  is  always  given  as  true; 
also  that  its  "direction"  means  the  direction  it  blows  from. 

Similarly,  if  the  course  steered,  the  air  speed  and  the  force  and 
direction  of  the  wind  are  known,  the  track  and  ground  speed  can 
be  obtained. 

For  example:  Course  112°  true;  wind,  20  m.  p.  h.  from  60°  true; 
air  speed  90  m.  p.  h.,  find  track  and  ground  speed. 


FIG.  18. 

On  AB,  drawn  at  an  angle  of  112°  from  the  meridian,  lay  off  a  dis- 
tance representing  90  m.  p.  h.  air  speed,  AC.  From  C  lay  off,  down 
wind,  at  an  angle  of  60°  from  the  meridian,  a  distance  equal  to  20 
miles,  on  the  same  scale.  Join  A  and  D;  measure  the  distance 
between  them  and  the  angle  AD  makes  with  the  meridian,  and  you 
have  the  ground  speed  of  the  machine  and  the  true  bearing  of  the 
track.  In  this  case  they  are  80  m.  p.  h.  and  125° 

RADIUS  OF  ACTION  IN  A  GIVEN  DIRECTION. 

The  supply  of  fuel  in  an  airplane  is  necessarily  limited.  A  cer- 
tain amount  of  gasoline  will  supply  the  plane  with  fuel  for  a  certain 
time.  In  making  a  long  trip  in  a  certain  direction,  it  is  desirable 
to  consider  in  advance  whether  the  objective  falls  within  the  plane's 
"radius  of  action."  The  radius  of  action  in  a  given  direction  is 
the  distance  that  a  plane  can  fly  in  that  direction  and  still  return, 
using  a  certain  amount  of  fuel — that  is,  flying  for  a  certain  time. 
The  radius  of  action  may  be  found  as  follows : 

Given  the  air  speed  of  the  machine,  the  direction  and  speed  of 
the  wind,  and  the  number  of  hours'  fiight  possible  with  the  supply 
of  gasoline  known: 

• 


AERIAL  NAVIGATION. 


23 


(1)  Compute  the  ground  speed  out  and  the  ground  speed  in  as 
heretofore. 

(2)  With  these  values  known,  the  radius  of  action  will  he  the 
number  of  hours  times  the  product  of  the  ground  speeds,  divided 
by  the  sum  of  the  ground  speeds. 

For  example,  if  the  ground  speed  out  is  50  m.  p.  h.  and  the  ground 
speed  in  is  64  m.  p.  h.  and  the  number  of  hours'  flight  possible  with 
a  given  supply  of  fuel  is  5  hours,  the  radius  of  action  is 


=140  miles. 


The  proof  for  finding  the  radius  of  action  is  not  given. 

For  one  hour's  flight  the  radius  of  action  is  the  product  of  the 
ground  speeds  divided  by  the  sum  of  the  ground  speeds. 

An  allowance  of  25  per  cent  should  be  made  for  changes  in  the 
wind,  etc. 

BEARINGS. 

N 


FIG.  19. 
DEFINITION. 

The  bearing  of  a  point  B  from  a  point  A  means  the  angle  NAB 
measured  clockwise  from  north.  Thus  the  true  bearing  of  B  from 
A  is  the  same  as  the  true  course  from  A  to  B,  the  magnetic  bearing 
of  B  from  A  is  the  same  as  the  magnetic  course  from  A  to  B.  The 
compass  bearing  of  B  from  A,  however,  requires  special  consideration. 

When  the  airplane  is  in  flight  steering  a  given  course,  the  com- 
pass bearing  of  points  along  the  course  is  the  same  as  the  compass 
course  steered.  It  is  often  useful,  however,  for  the  sake  of  fixing 
one's  position  to  take  bearings  of  points  off  the  course  that  one  is 
flying,  say,  the  bearing  of  B  from  A  when  the  course  is  AC.  When 
reckoned  from  the  course  AC  the  compass  bearing  of  B  from  A  is 


24  AERIAL  NAVIGATION. 

not  the  same  as  the  compass  course  from  A  to  B.  The  reason  is 
that  deviation  depends  on  the  direction  that  the  airplane  is  head- 
ing and  not  on  the  direction  that  the  pilot  is  looking.  The 
deviation  corresponding  to  the  bearing  above  is  the  deviation  for 
course  AC  and  not  for  course  AB. 


FIG.  20. 
FIXING  THE  POSITION  OF  A  MACHINE. 

The  pilot  may  fix  the  position  of  his  machine  at  a  given  time  by 
its  position  relative  to  two  known  points.  This  is  easily  established 
by  takmg  the  bearings  of  the  two  points  from  the  machine. 

Since  both  bearings  can  not  be  taken  at  once  and  the  machine  is 
rapidly  changing  its  position,  it  is  advisable  to  choose  the  first  object 
well  on  the  bow  and  as  far  away  as  possible  in  order  that  its  bearing: 
may  change  as  little  as  possible  before  the  bearing  of  the  second 
object  is  taken.  The  time  of  the  observation  is  the  time  when  the 
second  bearing  is  taken.  If  the  objects  are  chosen  in  this  manner 
the  "fix"  of  the  machine  is  accurate  enough  for  most  purposes. 
The  course  of  the  machine  must  remain  unchanged  during  this 
process. 

To  illustrate,  suppose  for  convenience  that  the  machine  is  flying 
north.  At  2  o'clock  take  the  bearing  of  a  distant  object  A  well 
on  the  bow,  bearing  15°  say,  and  at  2.01  take  the  bearing  of  a  nearer 
object  B,  bearing  100°  say.  Then  the  position  of  the  airplane  at 
2.01  is  found  by  the  intersection  of  two  lines  bearing  195°  from  A 
and  280°  from  B.  These  last  bearings  may  be  found,  if  desired, 


AERIAL  NAVIGATION. 


25 


by  drawing  from  A  and  B  lines  parallel  to  ON  to  represent  north 
at  these  points. 

In  general,  given  the  bearing  of  B  from  A,  the  bearing  of  A  from 
B  is  found  by  adding  180°.  In  case  the  resulting  angle  is  more 
than  360°,  subtract  360°  from  it.  For  example,  the  bearing  of  B 
from  A  is  350°.  Then  the  bearing  of  A  from  B  is  530°,  which  is 
the  same  as  170°.  This  gives  the  same  result  as  if  one  had  sub- 
tracted 180°  from  the  first  bearing  and  so  one  might  follow  the  rule 
to  add  180°  to  the  first  bearing,  unless  the  result  is  greater  than 
360°,  and  if  this  is  the  case,  subtract  180°  from  the  first  bearing. 


0 


FIG.  21. 


INSTRUMENTS. 

BEARING  PLATE. 

The  bearing  of  an  object  from  the  machine  is  taken  conven- 
iently by  means  of  the  bearing  plate,  a  description  of  which  follows. 

This  instrument  consists  of  a  fixed  plate  open  in  the  center  with 
two  arrows  arranged  so  that  it  can  be  set  in  the  fore  and  aft  line  of 
the  machine. 

On  this  is  set  a  movable  flat  ring  marked  off  for  each  5°  from  0° 
to  360°  in  a  clockwise  direction  with  numbers  placed  at  the  marks 
10°,  20°,  etc.  (fig.  22).  Fixed  to  the  outer  plate  is  a  movable 
framework  with  wires  stretched  across  and  capable  of  being  rotated 
around  the  plate.  At  either  end  of  this  framework  are  placed  up- 
right pointers  to  facilitate  sighting. 

The  chief  use  of  the  instrument  is  to  take  the  compass  bearing 
of  an  abject. 

77023—18 4 


26  AERIAL  NAVIGATION. 

To  do  this,  read  the  compass  course  of  the  machine  and  set  the 
movable  ring  so  that  the  number  opposite  the  forward  arrow  is 
exactly  the  same  as  the  compass  course.  We  see  from  the  figure 


FIG.  22. 


FIG.  23. 


FIG.  24. 


that  the  bearing  plate  will  then  have  its  zero  mark  in  exactly  the 
same  direction  as  the  compass  north,  and,  as  long  as  the  course 
remains  the  same  it  can  be  used  as  the  compass  for  observing  the 


AERIAL  NAVIGATION.  27 

direction  of  any  object.  The  compass  itself  can  seldom  be  used 
for  this  purpose  as  the  field  of  view  around  it  is  often  restricted. 
The  movable  framework  can  be  placed  so  that  the  sights  or  pointers 
and  center  drift  wires  (the  wires  being  called  drift  wires,  as  will  be 
seen  later)  are  aligned  on  the  object. 


FIG.  25. 

The  reading  of  the  point  B  will  give  the  bearing  of  the  object  0 
as  read  from  compass  north.  Of  course,  the  horizontal  bearing  is 
given,  but  as  the  position  of  the  machine  is  relative  to  the  ground 
all  bearings  are  those  of  the  point  vertically  above  the  object. 
Now,  having  found  the  bearing  of  any  object  from  the  compass,  it 
will  require  to  be  corrected  for  deviation  from  the  course  and 
variation.  This  will  give  the  true  bearing  of  the  object. 

For  example:  Compass  course  200°,  var.  13°  W.,  dev.  7°  E., 
compass  bearing  of  an  object  is  120°.  Find  its  true  bearing. 


CB        120° 

Dev.   7°  E 
MB       127° 

Yar.  13°  W 
TB        114° 


taken  from  the  compass  course. 


This  gives  the  true  bearing  of  the  object  from  the  machine  to  be 
114°,  and  therefore  the  bearing  or  direction  of  the  machine  from 
the  object  is  180°  plus  114°  equals  294°. 

AIRCRAFT  COURSE  AND  DISTANCE  INDICATOR. 

The  aircraft  course  and  distance  indicator  (C.  D.  I.)  makes 
possible  the  solution  of  certain  problems  during  flight  without  the 
use  of  pencil,  parallel  rulers,  dividers,  etc. 


28  AERIAL  NAVIGATION. 

DESCRIPTION. 

This  instrument  consists  of  (1)  an  outer  ring  marked  every  5° 
from  0°  to  360°;  (2)  a  central  rotating  disk  whose  radius  is  marked 
to  represent  120  miles,  the  disk  itself  being  squared,  each  side  of  a 
square  representing  10  miles;  (3)  two  arms  A  and  B  pivoted  at 
the*  center  of  the  disk,  marked  to  the  same  scale  as  the  disk  with 
two  movable  pointers,  one  on  each  arm;  (4)  a  central  clamp  hold- 
ing the  instrument  rigid  when  set. 

PRINCIPLE    OF   INSTRUMENT. 

The  instrument  is  made  to  apply  the  following  principle:  A 
force  l  represented  in  amount  and  direction  by  AM  (equals  CD) 
plus  a  force  represented  (in  amount  and  direction)  by  MB  is  equal 
to  the  force  represented  (in  amount  and  direction)  by  AB.  In 
this  case  AB  is  called  the  " resultant"  of  the  two  " component" 
forces  AM  and  MB. 


For  example,  if  the  line  AM  is  1  inch  in  length,  and  represents  a 
wind  of  40  m.  p.  h.  blowing  from  A,  and  the  line  MB  is  2  inches  in 
length  and  represents  an  air  speed  of  80  m.  p.  h.  in  the  direction 
MB,  the  resultant  speed  is  about  60  m.  p.  h.  in  the  direction  AB. 

In  the  following  problems  we  shall  have  to  do  with  these  quantities: 

(1)  Speed  and  direction  of  the  wind. 

(2)  Ground  speed  and  track  (course  to  be  made  good). 

(3)  Air  speed  and  course  (true). 

It  may  be  noted  that  the  ground  speed  is  always  along  the  track, 
and  the  air  speed  is  always  along  the  course  (here  taken  as  "true"). 

The  direction  of  the  wind  is  given  relative  to  true  north,  and  rep- 
resents the  direction  from  which  the  wind  blows;  for  example,  a 
north  wind  is  blowing  from  the  north. 

RULES   FOR   USING   INSTRUMENT. 

The  following  rules  for  using  the  instrument  are  given,  as  it  is 
hoped  that  by  paying  strict  attention  to  them  confusion  may  be 
avoided: 


i  Or  a  velocity. 


AERIAL  NAVIGATION. 


29 


(1)  Arm  A  should  when  possible  represent  your  own  course  and 
air  speed. 

(2)  Always  keep  the  general  lines  of  the  situation  in  your  head. 

(3)  Check  each  example  by  the  idea  more  or  less;  for  example,  the 
ground  speed  will  evidently  be  greater  than  the  air  speed  if  the 
wind  favors  the  pilot  on  his  course. 


FIG.  27. 


•£•30. 


Problem  I:  To  find  the  speed  and  direction  of  the  wind,  given  the  track 
and  ground  speed,  course  (true)  and  air  speed. 

Examples:  Machine  steers  300°  at  50  miles.  Track  observed  to 
be  260°  at  70  miles.  Find  the  speed  and  direction  of  wind. 

(a)  Set  arm  and  pointer  A  to  course  steered  (true)  and  air  speed 
300°  and  50. 


30  AERIAL  NAVIGATION. 

(6)  Set  arm  and  pointer  B  to  course  made  good  and  ground  speed 
260°  and  70. 

(c)  Set  disk  so  that  arrow  is  parallel  to  line  AB. 

jfrrow  points  to  direction  in  which  wind  is  blowing,  215°,  there- 
fore wind  blows  from  35°.  Length  of  AB  is  speed  of  wind,  44  m.  p.  h. 

Problem  IT:  To  find  what  li  allowance  to  make  for  a  wind." 

Given  speed  and  direction  of  the  wind,  airspeed,  and  track  desired, 
to  find  course  (true)  and  ground  speed. 

Example:  Wind  NE.,  40  miles.  Machine  air  speed,  70  mile,6". 
Pilot  Dishes  to  make  good  a  path  W.  What  course  must  he  steer? 

(<i)  Set  arrow  on  disk  to  course  to  be  made  good  (track),  270°. 

(b)  Set  arm  and  pointer  B  to  direction  from  which  wind  is  blowing 
and  to  speed  of  wind,  45°  and  40. 

(c)  Set  pointer  A  to  air  speed  of  machine,  70. 

(d)  Revolve  arm  A  till  pointer  A  is  on  same  line  (parallel  to  arrow) 
as  pointer  B. 

Arm  points  to  the  course,  295°. 

The  distance  between  pointers  A  and  B  will  be  ground  speed,  91. 
(See  fig.  28.) 

Problem  ITT:   To  determine  the  ground  speed  when  the  direction  of  the 
wind  is  known . 

This  problem  is  useful  when  the  direction  of  the  wind  is  observed 
to  change  during  a  flight  or  when  the  direction  of  the  machine  is 
changed. 

Given  the  direction  of  the  wind,  true  course,  air  speed,  and  track, 
to  find  the  ground  speed. 

(fi)  Set  arm  and  pointer  A  to  true  course  and  air  speed,  say  north 
and  80  m.  p.  h. 

(b)  Set  arm  B  in  direction  of  track,  way  :WO°. 

(c)  Move  disk  until  arrow  shows  the  direction  of  the  wind,  say  60°. 

(d)  Set  pointer  B  where  parallel  to  arrow  from  A  cuts  arm   B. 
This  will  give  the  ground  speed  along  the  trac*'.  69  m.  p.  h. 

The  conditions  given  in  this  problem  allow  us  also  to  read  from 
the  indicator  the  speed  of  the  wind.  In  this  case  it  is  <0  m.  p.  h. 

In  case  it  were  desired  to  fly  directly  up  for  down)  wind,  the  wind 
speed  might  be  computed  as  above  and  then  subtracted  'or  added 
to  give  the  ground  speed. 


AERIAL  NAVIGATION. 


31 


ILLUSTRATIVE  PROBLEM. 

(This  problem  is  given  to  apply  some  of  the  foregoing  principles 
in  succession  to  a  particular  case.  The  explanation  is  made  quite 
full  in  order  that,  if  desired,  the  problem  may  be  read  in  connection 
with  the  Introduction,  page  6.) 

By  means  of  map  and  compass  the  pilot  proceeds  as  follows  to  lay 
out  his  course.  First  he  draws  a  straight  line  on  his  map  from  aero- 
drome to  destination.  Then  he  measures  this  distance  on  the  map. 
This  distance  is  a  matter  of  inches.  It  is  necessary  to  fly  a  matter  of 
miles.  He  finds  the  correct  number  of  miles  as  follows:  On  his  map 
is  printed  a  ''representative  fraction."  R.  F.  equals  1/200,000,  say. 
This  means  that  a  distance  on  the  ground  is  200,000  times  as  great  as 
on  the  map.  Let  us  suppose  that  the  distance  on  the  map  is  14  inches. 
This  means  that  the  distance  on  the  ground  is  200,000  times  14  inches. 


36' 


FIG.  29. 

Since  there  are  5,280  feet  or  63,360  inches  in  a  mile,  the  distance  on 
the  ground  corresponding  to  the  observed  distance  of  14  inches  on 
the  map  is  44  miles.  This  disposes  of  the  problem  as  far  as  distance 
is  concerned. 

The  direction  that  the  pilot  is  to  steer  is  determined  as  follows: 
First  he  measures  his  course  on  the  map  by  means  of  a  protractor, 
measuring  the  angle  from  the  meridian  indicated  on  the  map  to  the 
straight  line  along  which  he  is  to  fly.  It  is  not  always  advisable  to 
fly  a  straight  course,  but  we  will  suppose  it  to  be  so  in  this  case. 
He  finds  this  angle  to  be  36°  say,  and  therefore  his  "true"  course 
is  36°. 

This,  however,  is  not  the  course  which  he  will  steer  when  rising 
his  compass,  because  the  compass  does  not  point  true  north.  In 
France  a  compass  unaffected  by  local  magnetism  points  from  10°  to 
15°  to  the  west  of  true  north,  toward  the  magnetic  pole  of  the  earth. 


32 


AERIAL  NAVIGATION. 


The  amount  by  which  the  compass  differs  from  true  north  is  known 
as  its  variation  and  is  said  to  be  easterly  or  westerly  according  as  the 
compass  points  east  or  west  of  true  north.  Let  us  suppose  that  the 
variation  of  the  compass  at  the  pilot's  aerodrome  is  15°  west. 


One  might  suppose,  then,  that  his  course  would  be  his  "true'?J 
course  plus  15°  (36°  plus  15°  equals  51°),  and  this  would  be  the  case 
if  there  were  no  local  magnetism  in  the  airplane,  but  the  compass 
is  affected  by  the  iron  and  steel  in  the  plane,  which  deflect  the  needle 


FIG.  31. 


a  little  this  way  or  that,  according  to  the  way  the  ship  is  headed. 
It  must  be  borne  in  mind  that  the  compass  needle  tends  to  point  to 
"magnetic-"  north  regardless  of  the  direction  of  the  ship,  and  as  the 
machine  changes  direction  different  bodies  affect  the  compass 
needle;  for  example,  when  the  ship  is  flying  east,  magnetism  in 


AERIAL  NAVIGATION. 


33 


the  engine  may  pull  the  compass  needle  toward  the  east,  and  when 
flying  west,  to  the  west.  It  has  been  found  necessary  in  practice 
to  correct  the  compass  reading  for  this  ft  deviation ^  at  the  points 
north,  east,  south,  west,  and  the  points  halfway  between  them. 
The  deviation  for  other  points  may  be  computed  from  these.  (See 
page  41.) 

Let  us  suppose  that  the  deviation  corresponding  to  the  pilot's 
" magnetic-"  course  of  51°  is  3°  west.  This  means  that  the  "  com- 
pass*' course  is  3°  plus  51°,  or  54°,  and  this  is  the  course  which  the 
pilot  will  have  to  steer — or,  rather,  it  is  the  course  which  he  would 
steer  if  there  were  no  wind. 


FIG.  32. 

Let  us  suppose  now  that  there  is  a  wind  from  true  north  blowing 
20  miles  an  hour.  This  means  that  no  matter  in  what  direction  the 
airplane  steers  it  is  going  to  be  carried  in  a  southerly  direction  at 
the  rate  of  20  miles  per  hour.  It  is  evident,  therefore,  that  if  the 
pilot  wishes  to  reach  a  certain  destination  he  must  steer  to  the  north 
of  it  by  a  certain  amount. 

Let  us  compute  this  amount  graphically  by  protractor  and  ruler. 
A  wind  blowing  from  the  north  will  delect  the  machine  in  a  south- 
erly direction  by  an  amount  proportional  to  20.  From  the  aero- 
drome O  let  us  draw  a  line  OA  in  the  direction  of  true  south,  say 
2  inches  in  length.  This  will  represent  the  amount  that  the  wind 
delects  the  ship.  Our  problem  is  to  steer  a  course  from  A  which 
will  keep  us  on  the  desired  track.  With  A  as  a  center  and  a  radius 


34  AERIAL  NAVIGATION. 

• 

of  9  inches  proportional  to  the  speed  of  the  ship,  let  us  cut  the  track 
at  the  point  P.  Then  AP  is  the  direction  to  be  steered  by  a  plane 
going  90  miles  an  hour  to  stay  on  the  track  in  spite  of  a  north  wind 
blowing  20  m.  p.  h.  If  we  measure  the  angle  OAP  with  a  protractor, 
we  find  it  to  be  29°.  This  angle  represents  the  true  course,  allowing 
for  wind. 

From  the  true  course  we  may  find  the  compass  course  to  be  steered 
by  applying  the  proper  variation  and  deviation  getting  as  a  result 
29°  plus  15°  plus  3°  (supposing  the  deviation  corresponding  to 
magnetic  44°  to  be  the  same  as  for  magnetic  51°,  although  this  would 
not  always  be  the  case)  equals  47°,  the  compass  course  to  be  steered. 

To  find  the  time  that  it  will  take  to  make  the  trip  we  may  proceed 
as  follows: 

We  measure  the  line  OP  along  the  track  (corresponding  to  a  length 
of  9  inches  along  the  course  to  be  steered)  and  find  it  to  be  1\  inches. 
This  means  that  the  ground  speed  or  speed  along  the  track  is  75 
m.  p.  h.  Therefore,  to  fly  the  required  distance  of  44  miles  will 
take  35  minutes.  We  have  now  worked  out  the  compass  course 
that  the  pilot  will  steer  and  also  the  time  it  will  take  him  to  reach 
his  destination. 

CHECKS. 

No  matter  how  carefully  a  pilot  lays  out  his  course  and  uses  his 
instruments,  it  is  desirable  to  have  certain  rough  checks  on  his 
flight  with  regard  to  direction  and  distance.  The  mistakes  that 
inexperienced  pilots  make  in  4he  air  are  almost  incredible — such 
mistakes  as,  for  example;  getting  30  miles  out  of  the  way  on  a  10- 
mile  flight. 

With  respect  to  direction  a  pilot  may  check  his  flight  by  means  of 
the  sun  and  the  map.  On  most  flying  days  the  direction  of  the  sun 
may  be  observed,  and  if  the  course  is  known  the  sun  ought  to  be 
in  about  such  a  position  relative  to  the  direction  of  the  plane.  While 
the  compass  and  the  calculated  course  are  the  chief  things  of  impor- 
tance, an  occasional  observation  of  the  sun  will  prevent  a  pilot  from 
making  hrje  errors  in  direction.  Such  errors  will  also  be  prevented 
by  careful  observation  of  the  country  over  which  he  is  traveling 
and  comparison  with  his  map. 

Observation  of  the  country  and  the  map  will  also  prevent  large 
errors  with  respect  to  distance.  These  errors  may  also  be  prevented 
by  a  knowledge  of  the  time  required  to  make  the  trip.  Such  a 
check  on  his  flight  would  prevent  the  pilot  from  being  30  miles  out 


AERIAL  NAVIGATION.  .  35 

of  the  way  on  a  10  mile  trip,  for  if  lie  flew  for  the  proper  length  of 
time  (in  still  air)  so  large  an  error  would  be  physically  impossible 
no  matter  what  direction  was  taken. 

TECHNIQUE. 

In  order  to  take  navigation  out  of  the  realm  of  theory  and  make  it  a 
practical  matter  it  is  necessary  for  the  pilot  to  develop  his  technique 
in  certain  respects  to  a  high  degree  of  proficiency.  It  is  necessary  to 
develop  (1)  a  sense  of  direction;  (2)  a  sense  of  distance;  (3)  a  sense  of 
quantity  (proportion).  In  each  of  these  respects  the  pilot  should 
train  himself  by  numerous  exercises  over  a  long  period  of  time 
until  accuracy  becomes  a  matter  of  instinct.  The  exercises  required 
are  so  simple  and  so  nearly  alike  that  it  is  not  feasible  to  print  a 
large  number  of  them.  It  is  left  to  the  pilot  to  make  up  a  large 
number,  perhaps  hundreds  of  exercises  similar  to  each  of  these,  and 
to  train  himself  to  work  them  out  with  speed  and  certainty. 


FIG.  33. 
DIRECTION. 

The  first  exercise  consists  in  drawing  angles  between  0°  and  360°, 
guessing  at  their  size  and  checking  by  protractor  until  the  guesses 
are  fairly  accurate.     For  example,  how  many  degrees  is  a  certain 
angle. 
.  Check  by  protractor.     This  angle  is  about  320°. 

Second  exercise:  The  line  OP  from  O  to  P  bears  300°  by  compass 
(fig.  34).  Draw  a  line  (a)  bearing  north  (fig.  35),  (b)  bearing  150° 
(fig.  36). 

Third  exercise:  The  following"  exercise  is  for  the  purpose  of  pre- 
venting the  pilot  from  making  large  errors  in  direction.  The  direc- 
tion of  the  sun  may  be  observed  approximately  on  most  flying  days. 
At.  12  o'clock  noon  this  direction  is  about  south  regardless  of  the 


36 


AERIAL  NAVIGATION. 


season  of  the  year.  At  6  p.  m.  it  is  about  west;  at  6  a.  m.  about 
east,  etc.  Thus  knowledge  of  the  direction  of  the  sun  at  any  hour 
of  the  day  will  give  the  pilot  an  idea  of  where  to  expect  north  and 


FIG.  34. 


FIG.  35. 


FIG.  36. 


all  the  other  directions,  although,  of  course,  it  will  not  enable  him 
to  correct  small  errors  in  his  compass  nor  get  along  without  his 
compass.  Such  knowledge  may  also  keep  him  from  being  confused 


FIG.  37. 

at  moments  when  the  compass  is  unreliable,  say,  after  a  steep  bank 
or  after  emerging  from  a  cloud.  From  0  the  sun  is  in  the  direction 
OP  at  2  p.  m.  Find  the  direction  of  north  from  0.  (Fig.  38.) 

DISTANCE. 

First  exercise:  How  long  does  it  take  to  go  12  miles  at  80  m.  p.  h.? 
This  exercise  should  be  worked  out  mentally  so  as  to  be  approxi- 
mately correct,  as  follows:  At  60  m.  p.  h.  it  would  take  12  minutes. 


AERIAL  NAVIGATION.  37 

At  80  m.  p.  h.  it*  would  take  less  than  12  minutes,  perhaps  9.  The 
guess  should  be  checked  as  follows:  Since  the  time  is  inversely  pro- 
portional to  the  speed,  it  would  take  sixty-eightieths  of  12  minutes, 
equals  9  minutes.  Usually  the  guess  will  be  somewhat  out  of  the 
way,  but  the  pilot  should  practice  the  exercise  until  his  guess  is 
approximately  correct. 

Second  exercise:  Two  vertical  searchlights  are  5  miles  apart.  It 
takes  4  minutes  10  seconds  to  traverse  the  digtance  between  them. 
Required  the  ground  speed.  The  plane  is  evidently  going  more 
than  60  m.  p.  h.,  say  70,  for  a  guess.  To  check  the  guess  proceed  as 
follows:  4  minutes  10  seconds  is  250  seconds.  Five  miles  in  250 
seconds  is  1  mile  in  50  seconds.  There  are  3,600  seconds  in  an  hour. 
One  mile  in  50  seconds  means  72  miles  in  an  hour,  thereby  checking 
the  guess. 

Third  exercise:  How  far  can  one  go  in  10  minutes  at  90  m.  p.  h.? 
The  guess  is  15  miles  and  may  be  made  correctly  at  once  since  10 
minutes  is  one-sixth  of  an  hour,  and  one-sixth  of  90  is  15. 

Fourth  exercise:  It  takes  55  seconds  to  go  a  mile.  Required  the 
speed.  The  speed  is  more  than  60  m.  p.  h.,  say  70,  for  a  guess. 
Check  as  follows:  There  are  3,600  seconds  in  an  hour;  therefore,  if 
1  mile  is  traveled  in  55  seconds,  65  miles  will  be  traveled- in  an  hour. 

PROPORTION. 

Certain  exercises  in  proportion  are  implied  in  the  foregoing. 
Certain  others  are  required  when  laying  out  a  course  to  allow  for 
wind,  as  follows: 

First  exercise:  An  air  speed  of  70  is  represented  by  a  line  2  inches 
in  length.  What  line  represents  a  wind  of  20?  Answer:  Two- 
sevenths  of  2  inches. 

Second  exercise:  A  wind  of  15  is  represented  by  a  line  1  inch  in 
length.  What  line  represents  an  air  speed  of  90?  Answer:  Six 
inches. 

Third  exercise:  Ground  speed  65  is  represented  by  a  line  3  inches 
in  length.  What  line  represents  an  air  speed  of  75?  Answer: 
Seventy-five  sixty-fifths  of  3  inches. 

NOTE. — In  solving  these  examples  in  proportion  it  is  first  desirable 
to  decide  the  general  question  "more  or  less."  Thus,  in  the  pre- 
ceding exercise  it  is  first  desirable  to  realize  that  the  line  representing 
75  will  be  more  than  3  inches  in  length  before  working  out  exactly 


38  AERIAL  NAVIGATION. 

how  much  more.  In  the  first  exercise  the  line  would  be  less,  and 
about  one-third  of  2  inches. 

Fourth  exercise:  Free-hand  drawing  of  lines  in  different  directions 
proportional  to  different  numbers.  Check  by  means  of  ruler  and 
protractor.  For  example,  draw  two  lines  making  the  angles  30° 
and  230°,  respectively,  with  a  given  line  and  proportional,  respec- 
tively, to  the  numbers  5  and  2. 

The  pilot  should  also  have  facility  with  a  time  scale,  described 
under  "Map  reading.1' 

COMPASS  ADJUSTMENT. 

Compass  adjustment  is  the  process  of  eliminating,  as  far  as  possible, 
errors  of  the  compass  caused  by  the  magnetic  material  in  the  ship. 
This  adjustment  is  effected  by  swinging  the  compass  on  a  temporary 
or  permanent  swinging  base,  which  is  essentially  a  central  point 
with  the  magnetic. cardinal  and  quadrantal  points  laid  off  around  it. 
The  process  of  swinging  consists  in  bringing  the  plane  with  the 
compass  in  it  to  the  base  and  successively  heading  it  on  .each  point. 

A  temporary  swinging  base,  such  as  is  constructed  at  an  aerodrome 
near  the  fighting  line,  is  located  out  in  the  field,  at  least  50  yards 
away  from  any  magnetic  material.  The  center  is  marked  with  a  peg. 
By  means  of  a  prismatic  compass  (or  any  oth  r  type  with  sighting 
attachments)  set  up  over  this  central  p  g,  the  pcsi'ions  of  the  eight 
points  are  detrmin  d  and  marke  d  with  p  gs  or  stakes.  (It  takes  two 
men  to  do  this,  one  to  sight  and  on°  to  p  g.)  When  r  stablishc  d,  each 
stake  should  be  joiird  to  the  central  p  g  by  a  taut  cord. 

The  p  rman^nt  swinging  base,  such  as  is  us  d  at  factcri  s,  schools, 
and  p  rman^nt  aerodrome  s,  is  made  by  digging  a  circular  basin  20 
yards  in  diamet  r  and  about  1  foot  deep,  and  filling  it  with  cono\  te. 
When  leveled  and  s  t,  the  platform  thus  formed  is  marked  off  with 
the  cardinal  and  quadrantal  points  as  above,  the  lin:s  being  marked 
with  black  paint  inst  ad  of  cords  and  p  gs. 

Before  the  machine  and  coir  pass  are  taken  to  the  swinging  base  for 
the  adjustment,  the  coir  pass  must  be  car  fully  inep  ct  d  for  its 
mechanical  condition.  Three  points  are  particularly  to  be  observed : 

1.  Large  bubbl  s  should  be  elhonat  d. 

2.  The  card  should  hang  evenly  on  its  pivot. 

3.  Th^re  should  be  no  friction  in  the  bearing. 

The  t:st  for  the  last  is  to  deflect  the  needle  with  a  magnet  and 
release  it.  If  it  does  not  come  back  promptly  to  the  reading  that  it 


AERIAL  NAVIGATION.  39 

had  brfore  the  deflection,  there  is  friction,  and  the  compass  must  be 
replaced. 

The  position  of  the  compass  in  the  machine  has  been  worked  out 
and  standardized  for  each  type  of  machine  in  order  to  secure  the 
great  st  ease  of  reading  by  the  pilot,  the  gr;  at  st  conveni  nee  of 
adjustment,  and  the  least  unbalanced  influence  from  the  magnetic 
material  in  the  ship.  It  follows  that  the  coir  pass  must  be  in  the 
authorized  position  for  the  given  type  of  machine,  and  in  no  other. 

The  compass  being  prep-  rly  placed  and  in  good  working  order  the 
machine  is  set  up  on  the  cent  r  of  the  flying  base,  tail  raise  d  to  flying 
position  by  means  of  a  trestle.  A  plumb  line  is  dropped  from  the 
boss  of  the  prop  Her  and  another  from  the  tail  skid  or  the  center 
line  of  the  tail.  Now,  by  sighting  along  these  and  the  N.  line,  one 
can  point  the  machine's  nose  due  north  (magnetic)  and  ots  rve  the 
compass  reading.  If  this  is  not  zero,  magnets  can  be  set  ath wart- 
ship  in  holes  provided  in  the  compass  case,  in  such  a  manner  that 
the  deflection  will  be  neutralized.  This  is  called  compensation. 

Next  the  machine  is  turn:  d  so  as  to  head  exactly  east,  b  ing  sighted 
along  the  plumb  lines  and  the  stake  or  ground  line  as  before,  and  the 
compass  reading  is  again  taken.  In  this  position  the  error  will  be 
much  greater  than  in  the  N.-S.  position,  for  the  needle  is  lying 
transv  rse  to  the  lines  of  force  from  the  chi  f  source  of  magnetic 
attraction,  the  engine,  which  is  always  in  the  fore-and-aft  line  in  any 
single-motor  type  of  ship.  Hence  more  compensating  magnets  are 
requir  d  for  correcting  on  the  E.-W.  axis  than  on  the  N.-S.  axis. 
Th  se  magnets  are  plac-  d  fore  and  aft  in  the  compass  case  in  order 
to  act  at  right  angles  to  the  needle,  which  is  pointing  in  the  general 
direction  of  north;  that  is,  athwartship,  the  ship  having  been  turned 
one-quart  r  turn  to  the  right  or  east. 

The  deviation  being  corrected  on  N.  and  E.,  the  machine  is  sighted 
on  S.  and  W.  in  turn.  If  the  deviation  in  these  positions  is  no  greater 
than  3°,  it  is  best  not  to  compensate  for  it,  since  to  do 'so  would  only 
throw  out  the  already  correct  reading  on  N.  and  E.  If,  however,  the 
error  is  greater  than  3°,  it  is  best  to  compensate  half  the  error  Since 
the  deviation  on  E.  has  already  been  corrected  by  fore-and-aft 
needles,  alteration  of  those  needles  to  correct  the  deviation  on  W. 
will  create  an  error  on  E.  approximately  equal  to  the  correction  on 
W.  Hence,  by  halving  the  error  on  W,  we  distribute  it  equally 
between  E,  and  W.,  giving  each  a  small  amount. 


AERIAL  NAVIGATION. 


This  compensation  on  the  cardinal  points  as  explained  serves  to 
neutralize  the  effect  of  the  permanent  magnetism  in  the  ship,  i.  e., 
that  resident  in  those  hard  iron  and  steel  parts  which  acquired 
magnetism  in  the  process  of  manufacture  and  assembly.  In  addi- 
tion to  these  errors  there  will  still  be  errors  on  the  quadrantal  points, 
due  to  induced  magnetism  in  the  soft  iron  of  the  ship.  In  the  ordinary 
aero  compass  these  can  not  be  compensated  for.  What  is  done  is  to 
swing  the  ship  to  all  these  points  and  note  the  error  on  each,  along 
with  any  uncompensated  error  on  the  cardinal  points  on  the  devia- 
tion card. 

The  deviation  card  is  then  prepared  and  placed  conveniently  near 
the  compass,  so  that  both  may  be  read  by  the  pilot  at  the  same  time. 

DEVIATION  CARD. 

The  deviation  card  represents  the  minimum  to  which  the  devia- 
tion of  a  particular  compass  in  a  particular  machine  can  be  reduced 
by  properly  placed  magnets.  A  common  form  of  deviation  card 
follows: 


Magnetic  course. 

Deviation. 

N. 

0° 

0 

NE. 

45° 

4W. 

E. 

90° 

1  W. 

SE. 

135° 

5E. 

S. 

180° 

2E. 

sw. 

225° 

7E. 

w. 

270* 

2W. 

NW. 

315° 

3E. 

Compass  checked  by  - 

When  the  compass  reading  has  been  corrected  as  above  for  the 
points  0°,  45°,  etc.,  an  approximate  correction  for  points  10°,  20°, 
30°,  etc.,  is  made  by  interpolation,  assuming  that  the  amount  of 
deviation  changes  regularly  from  point  to  point.  To  illustrate  this 
process,  the  following  table  is  made  out  from  the  deviation  card 
given  above,  giving  the  readings  from  0°  to  90°,  and  from  230°  to 
270°.  The  completion  of  this  table  is  left  as  an  exercise. 


AERIAL  NAVIGATION. 

TABLE. 


41 


Magnetic 
course. 

Devia- 
tion. 

10° 

1°  W. 

20°  ' 

2°  W. 

30° 

3°W. 

40° 

4°W. 

50° 

4°  W. 

60° 

3°  W. 

70° 

2°  W. 

80° 

2°  W. 

90° 

1°W. 

230° 

6°E. 

240° 

4°E. 

250° 

2°E. 

260° 

0° 

270° 

2°W. 

This  form  is  being  supplanted  in  the  United  States  Air  Service  by 
another  which  is  purely  visual  and  saves  labor  of  calculation.  It 
consists  of  two  concentric  circles,  marked  off  in  degrees  like  the  com- 
pass card.  The  inner  circle  represents  magnetic  readings,  the  outer 
circle  compass  readings,  and  lines  are  drawn  in  by  the  compass  officer 
connecting  the  two,  to  indicate  the  appropriate  amount  of  deviation. 

It  is  desirable,  however,  to  have  great  facility  in  working  out 
problems  from  a  deviation  card.  It  is  not  necessary  to  interpolate 
for  angles  which  are  not  multiples  of  10°.  The  deviation  corre- 
sponding to  these  angles  may  be  taken  as  the  deviation  correspond- 
ing to  the  nearest  multiple  of  10°.  For  example,  using  the  table, 
the  deviation  for  42°  is  taken  as  the  deviation  for  40°  (4°  W.)  and 
the  deviation  for  87°  is  taken  as  the  deviation  for  90°  (1°  W.),  etc. 
The  card  and  table  just  given  will  be  used  in  the  following  examples: 

Example  1:  The  compass  reading  corresponding  to  magnetic  32° 
is  35°. 

Example  2:  Corresponding  to  magnetic  235°  we  have  compass  229°. 

It  may  also  be  assumed  without  large  error  that  the  deviation  corre- 
sponding to  compass  50°  is  the  same  as  for  magnetic  50°,  etc.  With 
this  assumption  the  table  may  be  used  as  follows  to  pass  from  compass 
to  magnetic  readings. 


42  AERIAL  NAVIGATION. 

Example  3:  Corresponding  to  compass  232°. is  magnetic  233°. 

Example  4:  Corresponding  to  compass  2(56°  is  magnetic  264°. 

Given  variation  13°  W.  and  the  deviation  card  and  table  above: 

Example  5:  Find  the  compass  readings  corresponding  to  the  true 
reading  0°,  340°,  5°,  350°,  175°. 

Example  6:  Find  the  true  readings  corresponding  to  the  following 
compass  readings:  0°,  10°,  190°,  350°,  13°. 

Example  7:  Given  course  250°,  compass  bearing  45°,  find  true 
bearing. 

Example  8:  Given  course  54°,  compass  bearing  72 °,  find  true 
bearing. 

Example  9:  Given  course  232°,  compass  bearing  21  °,  find  true 
bearing. 


AERIAL  NAVIGATION. 


PART  II. 

THE  MAP. 

INTRODUCTION. 

In  our  study  of  aerial  navigation  so  far,  we  have  been  concerned 
primarily  with  the  compass.  This  instrument  helps  us  to  find  our 
objective,  once  we  know  the  track,  but  it  can  not  determine  the 
track. 

The  map,  on  the  other  hand,  not  only  helps  us  to  stay  on  the  track 
as  we  go  along,  but  shows  us  what  track  to  take  in  order  to  arrive  at  a 
desired  point.  The  plan  for  a  flight  must  be  made  from  the  map. 
On  the  map  the  flight  is  taken  in  theory.  The  pilot  with  his  plane, 
engine,  and  compass  turns  this  theory  into  practice,  but  he  must  have 
exact  knowledge  of  the  course  to  be  made  good.  If  it  were  known 
only  in  a  general  way  that  Bruges  lies  somewhere  north  of  Ypres, 
Bruges  would  have  no  fear  of  bombing  raids. 

Without  maps,  long-distance  flying  would  be  a  hit-or-miss  per- 
formance of  the  worst  sort.  Every  voyage  would  be  a  voyage  of  dis- 
covery and  there  would  be  no  such  thing  as  proceeding  in  short 
order  to  a  point  determined  in  advance  unless,  of  course,  one  were 
familiar  with  the  route .  Without  maps  the  military  value  of  aviation 
would  be  little  or  nothing. 

The  chief  characteristics  of  the  map  are  as  follows: 

I.  Points  on  the  map  represent  points  on  the  ground  and  vice 
versa. 

At  once  two  problems  are  presented  to  the  aviator: 

(1)  Given  a  point  on  the  ground  to  locate  it  on  the  map. 

(2)  Given  a  point  on  the  map  to  locate  it  on  the  ground. 

If  a  point  on  the  ground  which  we  wish  to  study  in  its  relation  to 
other  points  (to  a  battery  of  155 's,  say)  is  not  on  the  map  already,  the 
aviator  must  put  it  on  the  map.  He  has  three  means  of  doing  this: 

43 


44  AERIAL  NAVIGATION. 

(1)  By  marking  his  map.1 

(2)  By  making  a  rough  sketch  showing  this  new  point  in  relation 
to  points  already  known.     (Not  common.) 

(3)  By  taking  a  photograph. 

The  last  is  the  best  and  most  common  means  of  putting  points  on 
the  map,  but  it  can  not  be  treated  here  as  the  subject  is  too  large. 
Since  this  is  the  case,  we  shall  consider  only  the  problem  of  finding 
a  point  on  the  ground  that  is  given  on  the  map.  This  division  of  our 
subject  will  be  called  LOCATION  OF  POINTS. 

II.  A  map  is  drawn  uto  scale."     Distances  and  dimensions  on  the 
ground  are  reduced  in  a  certain  proportion  as  with  building  plans  and 
working  drawings.     It  follows  that  map  distances  must  be  translated 
into  ground  distances  and  vice  versa  according  to  the  given  propor- 
tion.   This  gives  the  aviator  two  problems: 

(1)  Given  a  distance  on  the  ground  to  find  the  corresponding 
distance  on  the  map. 

(2)  Given  a  distance  on  the  map  to  find  the  corresponding  distance 
on  the  ground. 

The  first  of  these  is  more  important  when  we  are  making  a  map; 
the  second  when  we  are  using  a  map  already  made.  Therefore,  the 
second  problem  will  be  emphasized  when  we  treat  of  SCALES. 

III.  It  must  be  remembered  that  objects  on  the  ground  are  shown 
on  the  map  as  if  viewed  from  directly  above.    Distance  between  two 
points  on  the  map  means  horizontal  distance  and  not  distance  along 
the  slopes  of  the  ground.     So  a  plan  of  a  gable  roof  represents  the 
horizontal  distance  between  the  eaves  and  not  distance  along  the 
roof  from  eaves  to  ridgepole  and  down  the  other  side. 

But  how  are  elevations  and  depressions  to  be  represented  on  a 
map?  Evidently  they  can  not  be  given  by  distances  because  all 
distances  that  can  appear  on  the  map  are  accounted  for  already  as 
horizontal  distances.  Therefore,  irregularities  of  elevation  (hills, 
plateaus-;  watercourses)  are  represented  by  symbols  called  CON- 
TOURS, which  show  the  elevation  of  certain  points  and  lines  above 
mean  sea  level,  and  enable  us  from  these  to  estimate  the  elevation 
of  other  points.  From  contours  we  are  able  to  tell  whether  a  slope 
is  going  up  or  down,  whether  it  is  gentle  or  steep,  whether  a  certain 
neighborhood  is  a  plain  or  a  rolling  country  or  whatnot  with  respect 
to  elevation. 


1  This  is  the  same  problem  as  fixing  the  position  of  the  machine,  Part  I,  page  24. 


AERIAL  NAVIGATION.  45 

IV.  But  there  are  many  other  objects  on  the  ground  besides  ele- 
vations and  depressions  which  have  to  be  represented,  if  at  all,  by 
symbols.  Map  position  shows  where  a  thing  is,  but  not  what  it  is. 
For  military  purposes  it  is  convenient  to  have  certain  other  CON- 
VEN'f  IONAL  SIGNS,  as  well  as  contours.  -.  Thus  we  may  represent 
the  forest  of  Villers-Cotterets  by  a  green  patch  on  the  map;  we  may 
surround  Dickebiisch  Lake  by  a  blue  line;  we  may  represent 
barbed-wire  entanglements  by  XXXX;  machine-gun  emplacements 
by  M.  G.,  and  so  on. 

Orientation. — When  using  a  map  in  connection  with  the  ground 
which  it  represents,  it  is  best  to  " orient"  the  map.  This  means  to 
place  it  "square  with  the  world";  that  is,  so  that  any  line  on  the 
map  which  represents  a  certain  direction  on  the  ground  is  actually 
pointing  in  that  direction.  The  line  most  commonly  used  to  orient 
a  map  is  the  north  and  south  line,  either  true  or  magnetic,  although 
any  line  may  be  utilized.  One  very  common  error  made  in  orien- 
tation is  that  of  comparing  true  north  on  the  map  with  magnetic 
north  on  the  ground,  or  vice  versa.  Care  must  be  taken  to  compare 
true  north  with  true  north  only,  and  magnetic  north  with  magnetic 
north  only,  unless  the  proper  correction  has  been  made  to  work  from 
one  to  the  other.  Maps  which  have  no  north  line  marked  upon  them 
may  be  assumed  to  be  drawn  with  the  direction  of  true  north  parallel 
the  side  of  the  map  and  pointing  toward  the  top. 

The  pilot  usually  orients  his  map  by  means  of  the  bearing  plate. 
The  bearing  plate  is  set  so  that  its  zero  mark  coincides  with  the  direc- 
tion of  compass  north.  Deviation  of  the  compass  is  determined 
from  the  deviation  card  according  to  the  compass  course  of  the  ship. 
The  problem  may  then  be  stated:  Given  compass  north;  find  the 
compass  bearing  of  true  north  1  (or  magnetic  north).  This  has  been 
treated  in  Part  I  under  the  heading  "Bearing  plate."  When  the 
compass  bearing  of  true  north  is  found,  it  is  necessary  only  to  set 
the  drift  wires  of  the  bearing  plate  in  this  direction  and  to  make  the 
meridians  on  the  map  take  the  direction  of  the  wires. 

The  four  general  divisions  of  our  subject  that  have  been  indicated 
above  will  be  treated  in  the  order  scales,  conventional  signs,  con- 
tours, location  of  points,  as  follows: 

1  For  example,  if  the  compass  needle  allowing  for  variation  and  deviation  points 
10°  to  the  west  of  true  north,  then  true  north  bears  10°  to  the  east  of  compass  north; 
that  is,  the  compass  bearing  of  true  north  is  10°. 


46  AERIAL  NAVIGATION. 

SCALES. 

Every  map  should  have  in  some  form  or  other  a  scale  or  statement 
of  the  proportion  between  distance  on  the  map  and  distance  on  the 
ground.  A  scale  should  be  the  first  thing  that  the  pilot  lotfks  for 
as  he  starts  to  read  a  map.  It  may  be  indicated  in  three  ways: 

(1)  By  equation:    1  inch  equals  3  miles;  1  mile  equals  3  inches. 

(2)  By  graphical  representation:  Laying  off  on  a  straight  line  dis- 
tances that  correspond  to  a  certain  number  of  miles  or  kilometers. 

I 1 1 1  - I 

Miles..    01234 

FIG.  1. 

(3)  By  representative  fraction  (R.  F.),  for  example,  1/200,000. 
This  means  that  a  distance  of  1  inch  on  the  map  represents  a  distance 
of  200,000  inches  on  the  ground.     So  1/20,000  means  that  1  inch  on 
the  map  stands  for  20,000  inches  on  the  ground.     Evidently  the 
dimensions  of  an  object  on  the  second  map  are  ten  times  as  great 
as  on  the  first. 

Relation  between  scales. — The  special  advantage  of  the  R.  F.  is  that 
it -is  equally  significant  whether  we  are  dealing  with  British  maps 
which  speak  of  miles  and  inches  or  French  maps,  which  speak  of 
kilometers  and  centimeters.  It  is  often  convenient,  however,  for  the 
aviator  to  think  in  terms  of  so  many  miles  to  an  inch  or  so  many  inches 
to  a  mile.  If  he  is  using  a  French  map,  these  forms  of  the  scale  will 
not  appear  and  he  will  have  to  construct  them.  He  may  proceed 
as  follows:  There  are  63,360  inches  in  a  mile.  Therefore  the  fraction 
1/63,360  stands  for  1  inch  to  a  mile  or  1  mile  to  an  inch.  To  solve 
the  problem  in  inches  to  a  mile  for  a  given  representative  fraction, 
we  must  answer  the  question,  "Will  there  be  more  or  less  than  1  inch 
(to  a  mile),  and  how  much?  "  Since  1  inch  on  the  map  corresponds 
to  200,000  inches  on  the  ground,  the  map  will  evidently  have  less 
than  1  inch  to  a  mile,  and  exactly  63,360  divided  by  200,000  equals 
0.32  inch  to  a  mile. 

By  the  same  reasoning  it  appears  that  on  this  map  there  will  be 
more  than  1  mile  to  an  inch,  and  exactly  200,000  divided  by  63,360 
equals  3.16  miles  to  an  inch. 

Therefore,  to  determine  the  number  of  inches  to  a  mile  or  miles  to 
an  inch  corresponding  to  a  given  representative  fraction,  we  either 
divide  into  63,360  or  divide  by  it  according  to  the  idea  "more  or 


AERIAL  NAVIGATION.  47 

less."  As  a  check  on  the  correctness  of  our  work  we  may  notice 
that  3  miles  to  an  inch  is  about  190,000  inches  to  an  inch,  proving  at 
a  glance  that  we  are  not  far  out  of  the  way. 

If  it  is  desired  to  lay  off  accurately  the  scale  0.32  inch  to  a  mile 
and  our  foot  rule  is  graded  to  sixteenths,  we  may  get  a  reasonable 
degree  of  accuracy  by  using  the  scale  of  numbers — 

}=0.25  A=0.0625 

J=0.125          ^-0.0313 

from  which  it  appears  that  0.32  is  about  J  plus  -^  or  -^  of  an  inch, 
(Evidently  0.32  is  more  than  0.25  and  less  than  0.50.  It  is  less  than 
0.25+0.125=0.375.  It  is  about  0.25+0.0625=0.3125.)  The  error  is 
75/10,000  of  an  inch,  which  in  this  connection  is  small.  This  will 
give  as  accurate  a  scale  as  a  pilot  will  probably  need,  for  short 
distances. 

For  long  distances  the  corresponding  scale  would  be  3.2  inches 
equals  10  miles.  With  a  foot  rule  this  might  be  laid  off  as  3  rg-  inches 
equals  10  miles,  the  error  on  the  ground  amounting  to  only  200  yards 
or  so  in  10  miles,  and  in  air  work  this  error  is  considered  small.  For 
still  closer  approximation,  using  thirty-seconds  of  an  inch  (taking 
points  midway  between  sixteenths)  the  error  could  be  further  re- 
duced to  about  1  mile  in  1,000. 

There  is  also  a  simple  geometrical  method  for  solving  this  problem, 
but  it  will  not  be  given  here,  since  without  good  instruments  it  is 
not  as  accurate  as  the  arithmetical  method  and  the  arithmetic  scale 
if  forgotten  can  be  readily  found  through  successive  divisions  by  2. 

TIME  SCALES. 

(In  the  following  it  must  be  borne  in  mind  that  speed  and  m.  p.  h. 
refer  to  ground  speed  and  not  air  speed.) 

We  have  seen  that  map  scales  show  relations  between  distances  on 
the  ground  and  distances  on  the  map.  It  is  also  desirable  for  the 
pilot  to  have  a  scale  of  map  distances  in  terms  of  the  time  it  takes 
to  fly  them  at  different  ground  speeds.  The  value  of  tl^s  scale  is 
that  it  enables  the  pilot  to  measure  on  his  map  the  time  it  takes  to 
fly  from  point  to  point  without  computing  the  number  of  miles 
traveled.  If  the  time  is  known  and  the  pilot  has  a  supply  of  fuel 
for  a  certain  number  of  hours,  the  number  of  miles  in  the  trip  makes 
no  difference. 

The  time  scale  is  constructed  by  choosing  a  convenient  time  unit, 
for  example,  10  minutes,  and  laying  off  the  distances  which  may  be 


48  AERIAL  NAVIGATION. 

traveled  in  this  time  at  different  ground  speeds.  Suppose  the  R.  F. 
of  the  map  is  1/200,000.  This  amounts  to -0.32  inch  to  the  mile,  or 
3.2  inches  for  10  miles,  or  3.2  inches  for  10  minutes  at  60  m.  p.  h. 
ground  speed.  At  70  m.  p.  h.  ground  speed  we  are  going  £  as  fast  as 
before,  and  so  for  10  minutes  the  map  distance  will  be  JX3.2=3f 
inches  (about) .  At  80  m.  p.  h.  ground  speed  we  are  going  |  as  fast  as 
at  60  m.  p.  h,  and  the  corresponding  map  distance  for  10  minutes 
will  be  4J  inches.  At  90  m.  p.  h.  ground  speed  the  map  distance 
is  4.8  inches,  and  so  on.  The  completed  scale  is  on  page  49. 

It  must  be  remembered  that  the  length  on  the  scale  from  zero  to  a 
certain  ground  speed  is  the  map  distance  traveled  in  10  minutes  at  that 
speed;  for  example,  referring  to  the  map  of  Paris,  a  plane  going  at 
the  rate  of  70  m.  p.  h.  ground  speed  could  fly  in  10  minutes  from 
Notre  Dame,  in  Paris,  to  St.  Germain,  about  3|  inches,  regardless  of 
the  number  of  miles  traveled  over  the  ground. 

So  in  20  minutes  at  the  same  ground  speed  7J  inches  map  distance 
might  be  covered;  for  example,  from  Chateau-Thierry  to  Soissons. 

To  find  the  time  required  to  fly  from  Paris  to  Soissons  at  90  m.  p.  h. 
ground  speed,  find  the  number  of  times  that  the  distance  from  0  to 
90  on  the  scale  will  be  contained  in  the  given  map  distance.  This 
number  of  times  turns  out  to  be  4.  Therefore  at  90  m.  p.  h.  ground 
speed,  it  will  take  about  4X10  minutes  for  the  flight. 

To  fly  from  Paris  to  Meaux,  a  map  distance  of  8  inches  at  90  m.  p.  h. 
ground  speed  will  take,  applying  the  tune  scale,  about  2JX10 
minutes,  equals  23  minutes. 

These  examples  may  be  worked  out  to  whatever  degree  of  accuracy 
is  required  by  the  circumstances;  for  example,  in  the  foregoing,  23 
minutes  would  be  a  sufficient  degree  of  accuracy. 

On  the  time  scale  it  will  be  found  that  60  is  twice  as  far  from  0  as  30 
and  that  120  is  twice  as  far  from  0  as  60,  etc. ;  that  is,  the  rate  repre- 
sented is  proportional  to  the  distance  from  0  on  the  scale.  For  this 
reason  interpolation  may  be  easily  applied;  for  example,  55  would 
lie  half  way  between  50  and  60,  and  so  on. 

If  desiftd,  any  other  convenient  unit  of  time  might  be  used 
instead  of  10  minutes;  for  example,  12  minutes.  If  the  scale  is 
graduated  for  10  minutes  on  one  edge  and  for  12  minutes  on  the 
other,  it  will  be  easy  to  compute  the  ground  speed  for  any  short 
distance  since  any  one  of  the  numbers,  2,  3,  4,  5,  6  is  contained 
either  in  10  or  12.  For  example,  a  pilot  finds  that  he  has  covered  a 
certain  map  distance  in  6  minutes.  Using  the  12-minute  scale  he 


o 

—  PJ 


o. 
o> 


8- 


in 


60 
M/A/LfTIS 


2.00, 


60 


50 


<D 


CM 

N. 


8 


<b 
QJ 


J- 

o: 


%• 


V 

Q) 
Q> 

.^ 


^  a* 

&* 


49 


50  AERIAL  NAVIGATION. 

finds  that  the  corresponding  distance  on  the  scale  shows  the  speed 
of  65  m.  p.  h.  It  follows  that  his  ground  speed  is  130  m.  p.  h.  In 
examples  of  this  sort  the  idea  "more  or  less"  must  be  kept  in  mind; 
for  example,  if  the  time  is  less  to  go  a  certain  distance,  the  speed  is 
more,  and  so  on. 
Other  examples  similar  to  the  above  should  be  worked  out. 

METRIC  SYSTEM. 

An  aviator  should  be  familiar  with  the  metric  system,  since  this 
system  is  used  on  French  and  Italian  maps.  Paragraph  2  of  General 
Orders  No.  1,  January  2,  1918,  reads  as  follows  : 

"The  metric  system  has  been  adopted*  for  use  in  France  for  all 
firing  data  for  artillery  and  machine  guns,  in  the  preparation  of 
operation  orders,  and  in  map  construction.  *  *  *  Instruction 
in  the  metric  system  will  be  given  to  all  concerned  *  *  *." 

For  quick  and  fairly  accurate  results  the  following  relations  suffice 
to  connect  the  metric  system  with  the  English  : 

1  centimeter  =f  inch. 
5  centimeters  =2  inches. 
10  centimeters=4  inches. 
1  meter  =1  "long"  yard. 
100  yards  =90  meters. 
200  meters=220  yards. 
1  kilometer=| 


10  kilometers  =6  miles. 
10  miles=16  kilometers. 

More  exact  relations  are  as  follows: 

1  inch=2.54  centimeters. 
1  centimeter  =0.4  inch. 
1  yard  =0.9  meter. 
1  meter  =1.1  yards. 
1  mile=1.6  kilometers. 
1  kilometer=0.62  mile. 

A  good  way  to  familiarize  one's  self  with  the  metric  system  is  to 
construct  geometrical  figures,  such  as  circles,  squares,  etc.,  of  known 
dimensions  in  inches  and  then  change  the  dimensions  to  centimeters. 
Another  way  is  to  measure  with  a  meter  stick  ordinary  objects  in  a 
room,  such  as  desks,  chairs,  tables,  etc.  It  is  often  useful  also  to 
pace  off  a  distance  previously  measure^  in  meters. 


AERIAL  NAVIGATION.  51 

The  following  examples  are  given  for  practice  on  scales  with 
English  and  metric  systems: 

Examples. 

(1)  If  a  map  is  made  on  a  scale  of  6  inches  to  the  mile,  give  the 
R.  F.  of  the  map. 

(2)  Construct  a  graphical  scale  of  miles  for  a  map  whose  R.  F.  is 
1/200,000. 

(3)  The  distance  between  two  towers  on  the  map  is  10  inches.    If 
the  R.  F.  of  the  map  is  1/200,000,  what  is  the  actual  distance  in 
kilometers  on  the  ground? 

(4)  Two  points  on  the  ground  are  10.5  kilometers  apart.    What  is 
the  distance  between  them  in  inches  on  a  map  whose  R.  F.  is 
1/100,000? 

(5)  Two  points  are  6  inches  apart  on  a  map  whose  R.  F.  is  1/40,000. 
Give  the  distance  on  the  ground  in  miles. 

(6)  (a)  The  scale  of  a  map  is  3  inches  to  the  mile.     Give  its  R.  F. 
(6)  To  what  French  map  does  it  correspond? 

(7)  The  distance  between  two  trees  is  measured  and  found  to  be 
500  yards;  on  the  map  they  show  to  be  2  inches  apart.    What  is  the 
R.  F.  of  the  map? 

(8)  If  two  points  are  6.7  inches  apart  on  a  map  whose  R.  F.  is 
1/100,000,  find  the  distance  in  miles  (kilometers). 

(9)  The  scale  of  the  map  is  1/20,000.    2.7  inches  on  that  map  equal 
how  many  miles  on  the  ground? 

(10)  Express  the  scale  1/10,000  graphically  in  terms  of  yards. 

(11)  A  map  is  48  inches  square.     If  the  R.  F.  is  1/200,000,  what  is 
the  area  of  the  country  represented  in  square  miles? 

(12)  Traveling  at  the  rate  of  150  m.  p.  h.  ground  speed,  what  would 
be  the  map  distance  in  inches  for  a  20-minute  flight  given  a  10-minute 
time  scale  and  a  1/200,000  map? 

(13)  Traveling  at  the  rate  of  120  m.  p.  h.  ground  speed,  what  would 
be  the  map  distance  in  inches  for  a  20-minute  flight  and  a  1/200,000 
map? 

(14)  Two  points  on  the  ground  are  10  kilometers  apart.     Find  the 
distance  in  inches  on  a  1/200,000  map. 


52  AERIAL  NAVIGATION. 

CONVENTIONAL  SIGNS. 

Conventional  signs  should  fulfill  two  requirements:  (1)  They 
should  be  as  simple  as  possible;  (2)  they  should  suggest  the  objects 
represented . 

The  number  of  these  signs  in  use  is  large;  a  few  of  the  most  im- 
portant ones  appearing  on  military  maps  are  presented  here.  Prac- 
tice with  the  map  should  be  given  until  the  student  is  perfectly 
familiar  with  them. 

Standard  abbreviations  of  letters  or  groups  of  letters  are  often  used 
in  connection  with  conventional  signs.  No  attempt  will  be  made 
to  present  these  here,  as  the  student  will  soon  be  accustomed  to 
those  in  use  upon  the  maps  with  which  he  is  working. 

It  should  be  remembered  that  the  list  of  conventional  signs  given 
below  is  general,  and  that  any  particular  map  must  be  studied  care- 
fully with  a  view  to  the  signs  which  appear  on  that  map. 

CONTOURS. 

The  earth  looks  quite  flat  to  an  aviator  at  any  considerable  distance 
above  it.  He  is  unable  to  tell  whether  it  is  sloping  up  or  down  or 
whether  he  is  passing  over  a  hill  or  a  valley  or  le\;el  country.  For 
this  reason  the  contour  lines  on  his  map  are  of  special  value. 

Contours  are  lines  obtained  by  cutting  the  earth's  surface  by 
horizontal  planes  at  certain  distances  from  each  other.  These 
distances  are  taken  at  convenience.  The  contours  are  marked  on 
the  map  to  show  their  distances  above  a  certain  plane  of  reference 
(datum)  usually  taken  as  mean  sea  level.  A  system  of  contours 
may  be  illustrated  by  considering  an  island  in  the  center  of  a  body 
of  water.  (See  figs.  3  and  4.)  The  shore  line  is  a  contour.  Imagine 
the  surface  of  the  water  to  be  raised  a  distance  of  10  feet.  The 
shore  line  thus  formed  is  a  contour  whose  elevation  is  10  feet  above 
the  first.  Successive  contours  representing  equal  increases  in  ele- 
vation can  be  secured  in  a  similar  manner.  These  contours  when 
projected  upon  a  single  plane  represent  a  contour  map.  (See  figs. 
5  and  6.)  The  vertical  distance  between  the  successive  elevations 
is  known  as  the  contour  or  vertical  interval  (abbreviated  to  V.  I.). 
The  distance  measured  on  the  map  between  two  successive  contours 
is  called  the  map  distance. 


CONVENTIONAL   SIGNS 
BRITISH 


J    \J    U    W    V/    I 

j  —   —  i 

Infantry,  moving  in  column  of  route 

L^L 

Any  trench  organized  for  fire 

L^-T- 

Cavalry,  moving  in  column  of  route 

Approximate  line,  reported  by 

zr     -=— 

Artillery,  moving  in  column  of  route 

•  —  •  —  .  —  - 

observers  and  not  yet  confirmed 

[J] 

Post 

by  photographs 

J* 

Patrol 

X  XXXX 

Wire  entanglements 

C±J  l±H  1  l|l 

Holding  line  in  action 

^SiSi) 

Ground  cut  up  by  artillery  fire 

oooo 

Gun  emplacements 

O 

Battery  of  guns,  inactive 

_,_.._._,_ 

Enemy  tracks 
Buried  pipe  line  or  cable 

V_y 

O  O  O 

Single  guns,  inactive 

Air  line 

T 

Battery  of  howitzers,  active 

A 

Supply  depot 

*4 

Single  howitzers,  active 

£ 

Observation  post 

At  ' 

Doubtful  battery,  active 

g 

Dugout 

^^ 

Doubtful  guns  or  howitzers,  active 

9 

Earthwork 

^^ 

Hedge,  fence,  or  ditch 

Q*  orM.G. 

Machine  gun  emplacement 

^^^D^ 

Ditch,  permanent  water 

®     orT.M. 

Trench  mortar  emplacement 

"©V0^0-0 

3=0=o=0^ 

Woods 

•  LorLP. 

[  istening  post 

0    O   ©   © 

* 

Mine  crater,  unfortified 

©  ©  © 

©   0 

Orchard 

"==  ==  "sJ^'rs11 

Brushwood  or  undergrowth 

Mine  crater,  fortified 

1  1  1  M  1  1  n  rt^T 

Faults  in  chalk  country 

Oo°o°o0 

Organized  shell  holes 

Embankment 

m-rrmnrrrr 

0r 

Anti-aircraft  gun 

4- 

Cutting 

Hutments 

O 

Church 

."¥" 

Aerodrome 

Wind  mil! 

fn?       1 

Airship  shed 

-0- 

Water  mill 

f 

Balloon 

^—^r 
^/frTTft   Y/////)( 

Houses,  standing 
Houses,  ruined 

A 

Barge 

Fe"C«d     Unienced 

Roads,  1st  class 
Roads,  2d  class 



p 

Fire 

Roads  3d  class 

® 

Railhead 

—  —  . 

Railways,  double 

r"H-» 

Mechanical  transport,  moving 

'           •          t^ 

Railways,  single 

Pg-v 

Mechanical  transport,  stationary 

,  ,  ( 

Narrow  gage  railway 
Trench  railway 

.|     j  —  * 

Horse  transport,  moving 

.^erry     ^^ 

Ferry 

|—  i 

Horse  transport,  stationary 

^^^ 

Railway  over  river 
Marsh 

CONVENTIONAL   SIGNS 
FRENCH 


German 

I:;;;;;     National  road 

loopholes  *•«$!* 

Repjrtmenta,    .     .        ,  .h 

<VV^K£fe! 

D'rt       d 

>|l|  °^E|O      7> 

jPSW 

Trenches 

—  •  Path,  cleared  line 
-S3—  e£S£    Standard  gage  single  track  R.R. 

ssJornsJ- 

**-~-*-CT^    Narrow  gage  R.  R. 

Trenches,  from  report 

8^I>r'd6e 

^W^B^?   Large  stream 



Trenches,  abandoned 

—  K  —  ^  —  -)f-   Small  stream 

Isolated  '     '      I      \ 

Batteries 

11     1  '      Canal 

painP  -*-*--*—  1 

Towpath 

•® 

Anti-aircraft  gun 

P°nd 

Camp. 

o            Spring 

•  ••   ^^ 

Camps,      Wag°"Parks 

©             Well 

••••s 

Munition  depots 

Err:  UKa^  Inundated  land 

J~-rv-^^v 

^S"*-^r-  \      Wall 

Works 

CV^vrx~X 

o-  •-0----0---  o    Hedge 

xxxxxx 

Wire  entanglements 

—  r  —  T  —    Iron  wire  fence 

m/mmm 

Abatis 

i  i  i  i  i  i  i  I  i  i  i  i  i  i  \  I    Earth  embankment  or  fill 

IZIadZb 

Shelters 

^^/2^ 

oob.  ap.c 

Screened  gun  pits 
Observation,  post  commanders 

^^^m    Vi"age 

©  ©  o 

Shell  or  mine  craters 

0            ©       Steeple 
+             i       Wayside  cross 

AM     &B 

Machine  guns,  bombthrowers 

6             <•)       Chapel 

XCR      \ 

Revolving  cannon 

l*tt|           Cemetery 



Standard  gage,  R.  R. 
Narrow  gage,  R.  R. 

•{J            Water  mill 

French 

O             Smokestack 

-  —  ..  ,,jni.^ 

Advanced  line 

W'/A          Vines 

m 

Infantry 

^jjitil      ['•'•'•'.|    Gardens  and  orchards 

& 

Cavalry  squadron 

^?^;S/?6-:^  Woods 

r 

|^A^/j          Fir  or  pine  thicket 

•B 

Cavalry  regiment 

&  ;:^v  •'-'        Brush 

•m 

Field  battery,  occupied 

o^o   o    o    o       |so)ated  trees 

t±±i 

Field  battery,  prepared 

-i^~>  ^r*.      Marsh  or  swamp 

ICXDl 

Aero  squadron 

/^^[iej^n     Contours  and  elevations 

ICXDj 

Aero  park 

—  •—  >* 

/^? 

>^!3    O      Sand  dunes 

vJ 

Balloon 

I^<7\ 

• 

^^      Quarry 

P     ^ 

Automobile  service 

,IM..,,,mi..-rr      g^gp   s|0pes 

AERIAL  NAVIGATION. 




53 


FIG.  3. 


FIG.  4. 


FIG.  5. 


54  AERIAL  NAVIGATION. 

In  general,  a  contour  is  quite  irregular  in  shape  although  every 
point  of  it  is  at  the  same  distance  above  mean  sea  level.  To  make 
the  matter  clearer,  let  us  illustrate  by  a  square  pyramid  placed  on 
a  table.  Let  the  surface  of  the  table  be  the  datum.  Let  the  vertical 
interval,  V.  I.,  be  taken  as  1  inch.  Imagine  the  pyramid  cut  by  a 
horizontal  plane  1  inch  above  the  table  top.  The  line  of  intersec- 


FIG.  6. 

tion  (contour)  is  a  square,  every  point  of  which  is  1  inch  above  the 
table.  This  square  might  be  called  "the  1-inch  contour."  If  we 
pass  another  plane  through  the  pyramid  2  inches  above  the  table, 
we  have  a  smaller  square  every  point  of  which  is  2  inches  above  the 
table.  This  square  is  "the  2-inch  contour." 


FIG.  7. 

If  we  replace  the  pyramid  by  a  circular  cone  and  pass  horizontal 
planes  as  before,  the  contours  will  be  circles.  If  we  replace  the 
cone  by  a  triangular  pyramid  the  contours  will  be  triangles,  and  so 
on. 

By  means  of  contours  on  a  map  it  is  possible  to  form  a  fair  idea  of 
the  general  appearance  of  ground  we  have  never  seen.  For  example, 


AERIAL  NAVIGATION. 


55 


we  can  tell  that  one  object  must  be  higher  than  another  because  it 
is  on  a  higher  contour.  We  can  tell  that  a  slope  is  steep  because  the 
contours  are  close  together,  or  that  it  is  gentle  because  the  contours 
are  far  apart,  or  that  there  is  very  little  change  in  elevation  on  the 
ground  because  the  contours  are  not  a  prominent  feature  of  the  map. 

So  far  we  have  been  considering  elevations.  Contours  serve 
equally  well  to  show  depressions.  For  a  downward  slope  proceed- 
ing in  a  certain  direction  the  elevation  of  the  contours  becomes  less 
and  less  as  we  go  along.  For  example,  if  the  vertical  interval  is  10 
meters,  the  contours  along  the  slope  might  be  numbered  150,  140, 
130,  etc.,  while  evidently  for  an  upward  slope  they  would  be  num- 
bered in  the  "reverse  order. 

If  the  contours  are  not  numbered  at  the  place  on  the  map  which 
we  are  studying,  it  may  be  possible  to  determine  whether  the  ground 
is  sloping  up  or  down  by  the  appearance  of  rivers  or  streams,  which 
branch  toward  their  sources  and  not  in  the  direction  they  are  flowing. 


FIG.  8. 

It  follows  that  the  point  A  in  figure  8  is  higher  than  point  B, 
although  the  contours  are  not  marked. 

The  more  irregular  the  country  which  we  wish  to  represent,  the 
closer  together  should  be  the  contours;  that  is,  the  smaller  should 
be  the  contour  interval  in  order  that  small  irregularities  may  be 
shown.  The  scale  and  size  of  the  map  are  also  factors  of  importance 
in  determining  what  contour  interval  shall  be  taken. 

The  following  facts  about  contours  should  be  well  noted: 

(1)  Contours  are  continuous  closed  lines  (for  example  the  circles, 
squares,  and  triangles  referred  to  above).  If  a  contour  does  not  close 
upon  itself  within  the  limits  of  the  map,  it  means  that  the  map  is  not 
large  enough  to  show  the  entire  contour. 


56 


AERIAL  NAVIGATION. 


(2)  All  points  on  a  contour  are  at  the  same  elevation,  because  the 
contour  lies  in  a  horizontal  plane . 

(3)  Contour  lines  do  not  branch.     A  branch  or  spur  projecting 
from  a  contour  would  indicate  a  ridge  the  top  of  which  is  an  abso- 
lutely  level    " knife-edge."     This,    of   course,   is   never  found   in 
nature. 


FIG. 


(4)  Contours  of  different  elevations  do  not  cross  each  other  except 
in  the  case  of  an  overhanging  cliff,  and  this  case  is  so  rare  that  any 
case  of  crossed  contours  may  be  considered  an  error.  Contours  at 
different  elevations  may  approach  each  other  closely,  and  in  fact 
may  appear  as  one  line  in  the  case  ot  a  vertical  cliff. 


/ $/0/>e 

FIG.  10. 

(5)  When  the  contour  interval  is  constant  (as  it  is  on  most  maps) 
the  spacing  of  the  contour  lines  indicates  the  degree  of  the  slope; 
that  is,  the  nearer  together  the  contours,  the  steeper  the  slope; 
the  farther  apart,  the  gentler  the  slope;  if  the  contour  lines  are 
equally  distant  the  slope  is  regular. 


AERIAL  NAVIGATION. 


57 


(6)  Contours  are  usually  drawn  as  brown  lines. 

(7)  Dotted  contours  are  sometimes  inserted  at  odd  elevations  to 
show  special  features  of  the  country;  for  instance,  a  33-foot  contour 
dotted  might  be  inserted  between  the  30-foot  and  the  40-foot  contour. 


FIG.  11. 


(8)  It  is  customary  to  break  contours  when  crossing  roads,  rail- 
roads, etc.,  continuing  them  on  the  other  side. 


FIG.  12. 
Examples. 

The  following  examples  are  given  to  illustrate  the  principles  of 
conventional  signs  and  contours: 

(1)  Illustrate  by  means  of  10-foot  contours:  (a)  A  hill  of  75  feet 
elevation,  rising  for  the  first  30  feet  gradually  and  being  very  steep 
for  the  last  45  feet;  (b)  a  hill  of  the  same  elevation  rising  steeply  for 
the  first  30  feet,  gently  the  last  45  feet;  indicate  a  stream  on  the  last 
hill. 

(2)  Would  you  expect  to  find  a  small  contour  interval  or  a  large 
contour  interval  on  a  map  of  a  very  rugged  country?    Give  your 
reasons.- 


58  AERIAL  NAVIGATION. 

(3)  Represent  the  following  by  contour  sketches:  Valley,  hill, 
depression,  ridge,  steep  slope,  flat  slope,  gorge. 

(4)  Make  a  sketch  showing  two  streams  joining,  a  ridge  between  the 
streams  and  rising  from  them,  steep  ground  on  one  side,  gently 
sloping  ground  on  the  other. 

(5)  Using  the  conventional  signs  of  the  map  of  Belgium,  draw  a 
map  of  a  southward  sloping  plain  5  kilometers  square,  maximum 
elevation  20  meters,  with  an  elongated  ridge  rising  30  meters  above 
its  north  edge.     A  stream  flows  down  the  south  slope  to  the  sea.     A 
single-track  railroad  follows  the  south  base  of  ridge  and  crosses  under 
a  first-class  road  along  which  are  houses,  a  church,  windmill,  and 
several  trees.    A  footpath  leads  from  a  house  to  a  depression  near  by. 

(6)  Imagine  you  are  standing  at  the  intersection  of  the  roads  shown 
at  point  21395-29410,  map  of  Belgium.     Describe  briefly  the  topog- 
raphy of  the  surrounding  country  within  a  circle  of  radius  2  kilo- 
meters with  your  position  as  the  center,  the  description  to  be  based 
upon  the  contours  and  conventional  signs  shown  within  the  territory 
mentioned.     Which,  if  any  parts  of  this  country  would  not  be  visible 
from  your  position,  and  why? 

(7)  Imagine  you  are  walking  down  the  Hazebeek  stream  from 
point  21350^28840  to  its  junction  with  an  unnamed  stream  at  point 
21522-29130.    Describe  what  you  can  see  on  each  side  as  you  walk, 
judging  from  the  contours  and  conventional  signs  on  the  map. 

(8)  Imagine  you  are  riding  on  the  rai'road  from  Walkrantz  station, 
point  22285-29575,  to  the  depot  at  point  22323-29160.     Describe  the 
country  within  view  on  each  side  as  you  ride  along,  judging  from 
the  contours  and  conventional  signs  on  the  map. 

(9)  Imagine  you  are  flying  in  a  straight  line  from  the  town  of 
Dickebusch  to  the  town  of  Elverdinghe.     Describe  the  country 
over  which  you  fly,  judging  from  the  conventional  signs  and  contours 
as  shown  on  the  map. 

LOCATION  OF  POINTS. 

It  is  not  only  in  long  flights  that  accurate  navigation  is  necessary. 
Short  flights  often  require  special  precision  because  of  the  nature  of 
the  objective.  A  machine-gun  emplacement  or  an  ammunition 
dump  carefully  camouflaged  is  invisible  from  the  air  unless  the 
.aviator  knows  in  advance  exactly  where  to  look  for  it.  This  precise 
knowledge  is  furnished  him  on  maps  drawn  to  a  larger  scale  than 
those  used  for  cross-country  flights,  bombing  raids,  and  the  like. 


AERIAL  NAVIGATION. 


But  no  matter  what  map  is  used  the  principle  of  locating  a  point  is 
the  same.  It  consists  of  inclosing  the  point  first,  within  a  large 
square  designated  by  a  number  or  a  letter;  then  (British  system) 
within  a  smaller  square  inclosed  by  the  first,  and  so  on.  Finally 
there  comes  a  time  when  this  method  of  inclosure  within  squares 
has  been  carried  as  far  as  it  is  practical.  The  British  use  three 
inclosing  squares;  the  French  only  one. 

COORDINATES. 

The  last  square,  however,  be  it  large  or  small,  represents  an  area 
and  not  a  point.  A  point  is  fixed  by  its  relation  to  the  western  and 
southern  boundaries  of  the  square.  Perpendicular  distances  from 
these  boundaries  will  fix  the  point  exactly. 


N 


0 


M 

FIG.  13. 


Suppose,  for  example,  that  the  square  given  in  the  figure  is  10 
units  on  a  side  and  that  ON  gives  the  direction  of  north.  The  point 
A  is  3  units  to  the  east  of  the  western  boundary  and  5  units  to  the 
north  of  the  southern  boundary.  These  distances  are  called  the 
'  coordinates  of  the  point  A. 

Instead  of  fixing  the  position  of  the  point  by  distances  from  the 
boundaries,  we  may  fix  it  by  distances  along  the  boundaries  measured 
from  the  southwest  corner  of  the  square  as  a  point  of  reference.  For 
example,  the  point  A  might  be  fixed  by  (1)  the  distance  along  the 
southern  boundary  from  O  to  a  point  M  directly  south  of  A  (in  this 
case  3  units),  and  (2)  the  distance  from  M  to  A  (equal  to  the  distance 
along  the  western  boundary  from  0  to  a  point  directly  west  of  A, 
in  this  case  5  units). 


60 


AERIAL  NAVIGATION. 


When  stating  these  distances  it  has  become  conventional  to  state 
first  the  distance  along  the  southern  boundary  (from  the  western 
boundary)  and  to  state  second  the  distance  along  the  western  bound- 
ary (from  the  southern  boundary),  just  as  in  geometry  we  always 
state  the  x  coordinate  first  and  the  y  coordinate  second  when  locating 
a  point. 

Exercises. 

N 


FIG.  14. 


(1)  Give  the  "pin-point"  location  of  the  points  A,  B,  C,  D,  E, 
assuming  the  same  square  as  given  above. 


FIG.  15. 

(2)  Without  changing  the  position  of  the  page  "pin-point"  F,  G, 
H,  I,  K. 

(3)  Drawing  a  certain  square  and  taking  points  O  and  N  as  above, 
locate  the  points  whose  coordinates  are  5-5,  3-3,  0-0,  6-4,  9-2,  1-9. 

It  is  conventional  never  to  use  the  coordinate  10  because  a  per- 
pendicular distance  of  10  from  the  boundary  of  one  square  carries 
us  to  the  boundary  of  another  square.  For  example,  the  northeast 


AERIAL  NAVIGATION. 


61 


corner  of  a  given  square  would  not  be  located  as  10-10  with  reference 
to  that  square,  but  as  0-0  with  reference  to  an  adjacent  square 
lying  northeast  of  the  first. 

BRITISH  MAPS. 

Let  us  take  the  ordnance  map  of  Belgium,  1/20,000  as  an  example 
of  British  maps.  This  map,  which  is  part  of  a  system  of  maps, 
represents  a  section  13,500  yards  in  width  by  11,000  yards  in  height. 
For  convenience  in  locating  points  the  maps  in  the  system  are 
divided  into  a  series  of  squares,  the  first  row  being  lettered  A,  B,  C, 
D,  E,  F;  the  second  row  being  lettered  G,  H,  I,  J,  K,  L,  with  G  under 
A,  II  under  B,  etc.  On  this  map  only  the  squares  A,  B,  G,  H  are 
found.  On  the  adjoining  map  to  the  east  we  should  find  square 
C  matching  up  with  B  and  I  with  H. 


FIG.  16. 

Each  lettered  square  is  subdivided  into  30  or  36  smaller  squares. 
Always  there  are  six  squares  from  west  to  east  and  five  or  six  squares 
from  north  to  south.1  The  large  squares  lettered  A,  B,  C,  etc.,  are 
6,000  yards  wide  and  5,000  or  6,000  yards  high.  The  smaller  squares 
which  make  up  the  large  squares  are  numbered  from  1  to  30  or  36 
(fig.  17).  Each  small  square  is  1,000  yards  in  width  and  in  height. 
These  numbered  squares  are  divided  into  four  minor  squares 
whose  sides  measure  500  yards.  These  minor  squares  are  considered 
as  lettered  a,  b,  c,  d,  but  only  squares  numbered  6  are  actually  so 
lettered,  to  avoid  unnecessary  confusion  on  the  map. 


1  In  converting  the  French  and  Belgian  maps,  laid  out  according  to  the  metric 
measurements,  to  the  English  system  of  map  squaring  in  yards,  etc.,  the  grid  lines 
do  not  coincide,  and  this  discrepancy  in  the  English  map  is  compensated  for  by 
making  some  lettered  squares  contain  30  squares  and  others  36. 


62 


AERIAL  NAVIGATION. 


To  locate  a  point  within  a  small  square,  consider  the  sides  divided 
into  10  parts  (fig.  18)  and  define  the  point  by  taking  so  many  tenths 
from  west  to  east  along  the  southern  side  first,  and  then  so  many 
tenths  from  south  to  north,  the  southwest  corner  always  being  taken 
as  the  origin.  If  square  c  belongs  to  square  14  in  big  lettered  square 
H  (fig.  18),  then  the  designated  points  would  be  located  as  follows 

J  atH!4c60. 
K  at  H14d05. 
L  at  H14c05. 
NatH14cOO. 
R  at  H14c67. 


••19- 


-2J5- 


.3-. 


--2-1- 


•£-7- 


T30- 


b- 


-3f. 5v- 


-3-0 


T 


FIG.  17. 


It  will  be  noted  that  a  point  is  not  designated  as  10,  since  10  is 
the  0  of  the  next  square.  If  a  point  is  on  the  upper  horizontal  line  of 
the  square,  it  is  zero  of  the  square  above,  and  if  the  point  occurs  on 
the  right  line  of  the  square  it  is  zero  of  the  square  to  the  right.  Thus 
the  point  Z  would  be  located  as  H14a40,  Q  would  be  H14bOO,  and 
K  would  be  H14d05.  Since  each  small  square  represents  500  yards, 
more  accurate  locations  may  sometimes  be  desired ,  and  in  such  cases 
the  sides  of  the  small  lettered  squares  may,  in  imagination,  be 
divided  into  100  parts  instead  of  10  parts.  This  would  necessitate 
the  use  of  four  figures  instead  of  two  as  before.  Thus  point  G  would 
be  located  at  H14c3565  and  X  would  be  located  at  H14c0847,  de- 
noting 08  parts  east  and  47  parts  north  of  origin.  Use  0,  but  not  10; 
use  either  two  or  four  figures,  but  do  not  use  fractions,  as  8J,  4J,  etc. 


AERIAL  NAVIGATION. 


63 


R 

I 

£ 

!_ 

f 

* 

0 

* 

V 

^ 

,N 

J 

FIG.  18. 
FRENCH  MAPS. 

The  method  of  locating  a  point  on  a  French  military  map  is  by  ref- 
erence to  grid  lines,  which  are  1  kilometer  apart  each  way.  These 
lines  are  approximately  N.-S.  and  E.-W.,  though  not  exactly  so. 
They  are  designated  by  numbers  reading  from  west  to  east  and  from 
south  to  north,  as  in  the  following  figure. 


C. 


FIG.  19. 

Assuming  each  of  these  squares  divided  into  10  spaces  from  west  to 
east  and  10  spaces  from  south  to  north,  the  point  A,  figure  19,  would 
be  designated  as  2165-2925,  point  B  as  2173-2931,  and  point  C  as 
2178-2904. 

Under  certain  circumstances  there  is  no  confusion  caused  by  drop- 
ping the  first  two  figures,  making  the  location  of  point  A  read  65-25, 
point  B  73-31,  and  point  C  78-04.  It  must  be  remembered,  however, 
if  the  first  two  numerals  are  dropped,  that  every  10  kilometers  north, 
south,  east,  and  west,  there  will  be  points  designated  by  the  same 
numbers.  Whenever  there  is  danger  of  confusion  three  figures  are 
used,  as  165-925. 

In  actual  work  on  the  front  the  lines  of  the  grid  are  given  letter 
designations,  which  may  be  changed  from  week  to  week.  Point  A 


64  AERIAL  NAVIGATION. 

might  be  called  U5-S5  one  week  and  Q5-K5  the  following  week. 
In  this  way  the  enemy  is  kept  from  knowing  the  zone  to  which 
wireless  messages  may  refer.  Various  keys  of  letters  are  in  use,  and 
from  time  to  time  orders  are-  issued  substituting  one  for  another. 
In  using  this  letter  system  repetition  of  the  same  letter  would  occur 
every  25  kilometers  along  the  whole  front  (the  number  of  letters  in 
the  French  alphabet). 

Exercises. 

The  following  exercises  are  given  to  illustrate  the  practical  use  of 
compass  and  map: 

Example  1:  Fly  from  the  church  in  Elverdinghe  to  the  church  in 
Boesinghe,  to  the  church  in  Brielen,  and  back  to  the  starting  point. 
Make  a  diagram  of  the  course,  giving  the  magnetic  bearings  and  the 
names  of  the  places  with  the  pin-point  location  under  them.  Let 
an  arrow  indicate  the  direction  of  each  flight. 

Example  2:  Fly  from  the  church  in  Ypres  to  the  church  in  Voor- 
mezeele,  to  the  church  in  Dickebusch,  to  the  church  in  Vlamertinghe, 
and  back  to  starting  point.  This  will  make  a  four-sided  diagram. 
State  the  magnetic  bearing  of  each  line,  give  the  pin-point  location 
of  the  corners  of  the  course  under  their  names,  and  estimate  the 
length  of  each  course  in  kilometers. 

Example  3:  Fly  from  Goed  Moet  Mill  near  Ouderdom  to  the  church 
in  Reninghelst,  to  the  lower  church  in  Poperinghe,  to  the  crossroads 
in  Busseboom,  to  the  church  in  Vlamertinghe,  and  back  to  starting 
point.  Indicate  on  the  diagram  the  magnetic  bearing  of  each  line, 
the  name  and  pin-point  location  of  each  corner  of  the  course,  and 
the  length  of  each  course  in  kilometers. 

Example  4:  From  your  aerodrome  at  2175-2885  course  45°  (mag. 
bearing)  fly  to  a  point  4.5  kilometers  away.  Give  pin-point  of  the 
end  of  the  course. 

Example  5:  From  your  aerodrome  at  2175-2885  fly  3.5  kilometers 
course  60°  (mag.  bearing),  then  4  kilometers  course  300°,  then  back 
to  starting  point.  What  is  the  length  and  magnetic  bearing  of  the 
last  course?  Pin-point  the  other  two  corners  of  the  course. 

Example  6:  From  church  in  Reninghelst  course  10°  33X  fly  for 
a  distance  of  3.5  kilometers  and  from  there  fly  to  churcl}  in  Vlamer- 
tinghe. From  that  point  fly  back  to  starting  point.  Make  diagram 
showing  all  magnetic  bearings,  pin-point  corners  of  course  to  five 
places,  let  arrows  indicate  direction  of  flight,  and  give  distance  in 
kilometers  from  corner  to  corner  of  course. 

o 


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